Definitions for Unit Ten: Circles
Section 7 - 6
97. circle: the set of points in a plane that are equidistant from a given point. The given point
is the center. The distance from the center to a point on the circle is a radius. (The plural of
radius is radii.) Name a circle by using the center.
*Note: All radii within one circle are congruent.
98. chord: a segment that joins two points on a circle
99. diameter: a chord that passes through the center of a circle (diameter = 2 (radius))
100.
secant: a line that contains a chord (may also be a ray or a segment)
101.
congruent circles: circles that congruent radii
102.
concentric circles: circles that lie in the same plane and have the same center
103.
sphere: the set of points in space equidistant from a given point
104.
inscribed polygon in a circle: a polygon whose vertices lie on the circle. Its’
sides are chords of the circle. (The circle circumscribes the polygon.)
105.
tangent to a circle: a line in the plane of the circle that meets (Intersects) the
circle in exactly one point. This point is called the point of tangency.
106.
Common tangent: a line that is tangent to each of two coplanar circles
Common internal tangents intersect the segment joining the centers.
Common external segments do not intersect the segment joining the centers.
107.
tangent circles: two circles are tangent to each other when they are coplanar and
are tangent to the same line at the same point
108.
circumscribed polygons: a polygon in which a polygon is tangent to a circle.
The circle is inscribed in the polygon.
109.
central angle (of a circle): an angle whose vertex is the center of the circle
110.
minor arc: the set of points on a circle which lie on a central angle or in the
interior of the central angle. The measure of a minor arc is less the 180 and is defined
to be the measure of its central angle. A minor arc is named by its endpoints.
111.
semicircle: the union of the endpoints of a diameter and the points of the circle is
one of the half planes whose edge contains the diameter. The measure of a semicircle
is 180. Three letters (2 of which are the endpoints of the diameter) should be used to
name a semicircle.
112.
major arc: the points of a circle that are in the exterior of a central angle. Major
arcs are named with three letters. The measure of a major arc will always be greater
than 180.
*Note: measure of major arc = 360 – measure of a minor arc
113.
congruent arcs: arcs in the same circle or in congruent circles that have equal
measures
114.
adjacent nonoverlapping arcs: arcs that have exactly one point in common
Section 11 - 3
115.
inscribed angle: an angle whose vertex is on a circle and whose sides contain chords of the circle
116.
intercepted arc: an arc whose endpoints lie on different rays of an angle and
whose other points lie in the interior of the angle
Theorems for Unit Ten: Circles
Section 11 - 1
100. If a line is tangent to a circle, then the line is
101. (Corollary) Tangents to a circle from a point are
102. If a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the
line is
103. The sum of the opposite sides of a circumscribed quadrilateral are
Section 11 - 2
104. In the same circle or in congruent circles,
1.
2.
3.
105.. In the same circle or in congruent circles:
1.
2.
106.A diameter that is perpendicular to a chord
107.In the same circle or in congruent circles:
1.
2.
Section 11 - 3
108. The measure of an inscribed angle is equal to
109. (Corollary) If two inscribed angles intercept the same arc, then
110. (Corollary) An angle inscribed in a circle is
111. (Corollary) If a quadrilateral is inscribed in a circle, then
112. The measure of an angle formed by a chord and a tangent is
Section 11 - 4
113. The measure of an angle formed by two chords that intersect inside a circle is equal to
114. The measure of an angle formed by two secants, two tangents, or a secant and a tangent
drawn from a point outside a circle is equal to
115. When two chords intersect inside a circle, the product of the segments of one chord
equals
116. When two secant segments are drawn to a circle from an external point, the product of
one secant segment and its external segment equals
117. When a secant segment and a tangent segment are drawn to a circle from an external
point, the product of the secant segment and its external segment is equal to
Theorems for Unit Ten: Circles
Teacher Notes
Section 11 – 1
100.If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the
point of tangency.
101. (Corollary) Tangents to a circle from a point are congruent.
102.If a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the
line is tangent to the circle.
103. The sum of the opposite sides of a circumscribed quadrilateral are congruent.
Section 11 – 2
104.In the same circle or in congruent circles,
1. Congruent central angles have congruent arcs.
2. Congruent chords have congruent arcs.
3. Congruent arcs have congruent central angles.
105. In the same circle or in congruent circles:
1. Chords equidistant from the center are congruent.
2. Congruent chords are equidistant from the center.
106. A diameter that is perpendicular to a chord bisects the chord and its arcs.
107.In the same circle or in congruent circles:
1. a diameter that bisects a chord (that is not a diameter) is perpendicular to the chord.
2. the perpendicular bisector of a chord contains the center of the circle.
Section 11 - 3
108.The measure of an inscribed angle is equal to half the measure of its intercepted arc.
109.(Corollary) If two inscribed angles intercept the same arc, then the angles are congruent.
110.(Corollary) An angle inscribed in a circle is a right angle.
111.(Corollary) If a quadrilateral is inscribed in a circle, then its opposite angles are
supplementary.
112.The measure of an angle formed by a chord and a tangent is half the measure of its
intercepted arc.
Section 11 - 4
113. The measure of an angle formed by two chords that intersect inside a circle is equal to
half the sum of the measure of the intercepted arcs.
114.The measure of an angle formed by two secants, two tangents, or a secant and a tangent
drawn from a point outside a circle is equal to half the difference of the measure of the
intercepted arcs.
115.When two chords intersect inside a circle, the product of the segments of one chord
equals the product of the segments of the other chord.
116.When two secant segments are drawn to a circle from an external point, the product of
one secant segment and its external segment equals the product of the other secant segment
and its external secant segment.
117.When a secant segment and a tangent segment are drawn to a circle from an external
point, the product of the secant segment and its external segment is equal to the square of the
tangent segment.
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 68
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 How are the properties of circles and its components used?
 How are the measures of central angles, minor arcs, and major arcs found?
 How are arcs and angles named in circles?
Objective(s): NCSCOS 1.02 Use length, area, and volume of geometric figures to solve
problems. Include arc length and area of sectors of circles.
APK:
 Take up Cumulative Review.
 Go over Test.
 Do orally: Check Skills You’ll Need; page 386: 1 – 4 all
TIP/SAP:
 Distribute: Definitions for Unit Ten note guide.
 Define, explain, and give examples of: 1) circle, 2) chord, 3) diameter, 4)
secant, 5) congruent circle, 6) concentric circles, 7) sphere, 8) tangent, 9)
inscribed polygon in a circle, 10) central angle, 11) minor arc, 12)
semicircle, 13) major arc, 14) congruent arcs, 15) adjacent nonoverlapping
arcs.
 Examples: worksheet labeled: Section 9.1 Chalkboard Examples
 Students: Practice 7 –6: 4 – 8 all (workbook, page 44)
 Show how a pie graph uses central angles (Real World Connection). Do
together: page 380: 1 – 8 all
 Do together: Practice 7 – 6: 15 – 20 all (workbook, page 44)
GP:


(with a partner) page 390: 9 – 14 all, 16 – 26 even
Go over.


Page 390: 15 – 25 odd
Go over.
IP:
Assessment:
 Orally: page 391: 49 – 51, all
Homework:
 Page 391: 42 – 47 all, 52, 53
 Worksheet labeled: Section 9.1 Homework
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 69
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 How is the relationship between a radius and a tangent used?
 How is the relationship between two tangents from one point used?
Objective(s): NCSCOS 2.03 Apply properties, definitions, and theorems of two-dimensional
figures to solve problems and write proofs: d) circles.
APK:
 Go over homework.
 Check Skills You’ll Need: page 582: 1 – 6 all
 Go over.
TIP/SAP:
 Review: tangent to a circle, point of tangency, inscribed in, and
circumscribed about.
 State, explain, and give examples involving tangents and radii.
 Examples: page 586: 1 – 3 all
 Students: Practice 11 – 1: 1 – 3 all (workbook, page 66)
 Example: page 586: 4
 Students: Practice 11 – 1: 7 – 9 all (workbook, page 66)
 Examples: page 586: 10 – 12 all
 Students: Practice 11 – 1: 4 – 6 all (workbook, page 66)
 Examples: page 586: 13 – 15 all
 Students: Practice 11 – 1: 10 – 12 all (workbook, page 66)
 Example: page 586: 16
 Students: Practice 11 – 1: 13 – 15 all (workbook, page 66)
GP:


(with a partner) pages 586 – 587: 17 – 19 all; page 589: 43 – 46 all
Go over.
IP:


Worksheet labeled: Section 9.2: 1 – 7 odd
Go over.
Summarize/Assessment:
 Page 586: 20 – 22 all
 Turn in.
Homework:
 Complete worksheet labeled: Section 9.2
 Mixed Review: page 589; 48 – 55 all
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 70
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 How do you apply theorems relating chords with angles and arcs of
circles?
Objective(s): NCSCOS 2.03 Apply properties, definitions, and theorem of two-dimensional
figures to solve problems and write proofs: d) circles.
APK:
 Go over homework.
 Check Skills You’ll Need: page 590: 1 – 3 all
 Go over.
TIP/SAP:
 Review the definition of a chord of a circle.
 State, explain, and give examples of the theorems involving chords of a
circle.
 Examples: pages 593 – 594: 1 – 17 odd
 Students: pages 593 – 594; 2 – 18 even.
GP:


(with a partner) Practice 11 – 2: 1 – 11 all (workbook, page 67)
Go over.
IP:


Worksheet labeled: Section 9.5 (page 347: Wr. Ex. 1 – 9 all)
Go over.
Assessment:
 Worksheet labeled: Section 9.4 (chalkboard and guided practice)
 Take up.
Homework:
 Worksheet labeled: Arcs, Central angles, and Chords
 Mixed Review: page 596: 47 – 50 all
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 71
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 How are the properties involving arcs and angles of a circle applied?
Objective(s): NCSCOS 2.03 Apply properties, definitions, and theorems of two-dimensional
figures to solve problems and write proofs: d) circles.
APK:
 Go over homework.
 Check Skills You’ll Need: page 598: 1 – 8 all
 Compare answers with a partner.
TIP/SAP:
 Define, explain, and give examples of an: inscribed angle and intercepted
arc.
 Examples: page 601: 1, 2
 Students: page 601: 3
 State, explain, and give examples of theorems involving inscribed angles.
 Examples: worksheet labeled: Section 9.5 Chalkboard examples
 Students: worksheet labeled: Section 9.5 Guided Practice
GP:


(with a partner) page 601 – 602: 6 – 24 even.
Go over.
IP:


Practice 11 – 3: 1 – 13 odd (workbook, page 68)
Go over.
Summarize:
 Complete Practice 11 – 3: 2 – 14 even.
 Go over.
Homework:
 Mixed Review: page 605: 53 – 58 all
 Worksheet labeled: Section 9.5 (page 354: 1 – 9)
 Worksheet labeled: Tangents, Arcs, and Chords (take up for a quiz grade.)
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 72
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 How are the measures of angles other than central and inscribed angled
determined?
 How are the lengths of chords, secants, tangents and radii determined?
Objective(s): NCSCOS 2.03 Apply properties, definitions, and theorems of two-dimensional
figures to solve problems and write Proofs: d) circles.
APK:
 State, explain, and give examples of theorems relating other angles of a
circle.
 Discuss location of the vertex of the angle in relationship to the circle. If
the vertex of the angle is: 1) on the circle – measure of the angle = half the
measure of the intercepted arc. 2) inside the circle – measure of the
angles = half the sum of the intercepted arcs (or I say, add and divide by
two). 3) outside the circle – measure of the angle = half the difference of
the intercepted arcs (or I say, subtract and divide by two).
 Examples: worksheet labeled: pages 358 – 359: Cl. Ex. 1 – 9 all
 Students: page 611: 1 – 6 all
 State, explain and give examples of theorems relating measures of
segments of circles.
 Examples: page 611: 9 – 13 odd
 Students: page 611: 10 – 14 even
GP:



(with a partner) worksheet labeled: Section 9.6 (one circle with eight
questions)
Page 612: 20 – 25 all
Go over.


Worksheet labeled: Other Angles
Go over.
IP:
Assessment:
 Ticket Out the Door: Answer the EQ’s.
 Turn in.
Homework:
 Page 613: 38 – 47 all
 Practice 11 – 4 (workbook, page 69)
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 73
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 What concepts will be on tomorrow’s test?
Objective(s): NCSCOS 2.03 Apply properties, definitions, and theorems of two-dimensional
figures to solve problems and write proofs: d) circles.
APK:
 Go over homework.
 Lesson Quiz (page 612, TE)
 Go over.
TIP/SAP:
 Review finding angle measure in circles.
GP:

(with a partner) Worksheet labeled: Circles, Angles, and Arcs (36 angles)
(30 minutes)
IP:



Worksheet labeled: Circles and Lengths of Segments
Worksheet labeled: Angles and Segments
Go over.
Summarize:
 Answer the EQ.
Homework:
 Worksheet labeled: Circles
 Study for test.
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 74
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 How well did I do on today’s test?
Objective(s): NCSCOS 2.03 Apply properties, definitions, and theorems of two-dimensional
figures to solve problems and write proofs: d) circles.
APK:
 Go over homework.
IP:

Test on Unit Ten.
Homework:
 Complete worksheet labeled; Circles, Angles, and Arcs (take up for bonus
points on tests.)
Unit Ten Answer to Worksheets
Section 9.1 Chalkboard Examples
1. radius
2. chord
3. secant
4. diameter
5. tangent
6. tangent
7. point of tangency
8. TU
9. PQ , PQ
10. SU , SQ , SP , SR
Section 9.1 Homework
1. A
2. DB , FC
3. D
4. AD , AF , AB , AC
5. DE
6.
7. FC
8. DF , FB , BC , CD , DB , FC
9. A does not lie on the circle.
10. Chords are segments, not lines
14. 5
15. 6
16. 4 2
17. 5 2
Section 9.2
1. 9
2. 3 2
3. 10
4. 6 2
5. 8
6. 12
7. CDB, 55
8. 25
Section 9.4: page 347 (Wr. Ex.) 1 – 9 all
1. 8
2. 5
3.
4.
5.
6.
7.
8.
9.
9 2
55
80
45
24
12
10 5
Section 9.4 (chalkboard and guided practice)
1. 12, 12
2. 3 3 , 3, 120
3. 8, 16
4. 30, 8
5. 140, 70
6. 80
Arcs, Central Angles, and Chords
1. 90
2. 135
3. 135
4. 225
5. 45
6. 55
7. 20
8. 60
9. 150
10. 11 or 1
11. 12
12. 8 3
13. 60
14. 120
15. 120
16. 4 3
17. 9
18. 9
19. 24
20. 14
Section 9.5
1. x == 40, y = 75
2. x = 20, y = 20
3. x = 60, y = 50
4. x = 40, y = 50
5. x = 160, y = 100, z = 100
6. x = 30, y = 60, z = 150
7. x = 98, y = 49, z = 49
8. x = 9, m  D = 101
Section 9.5 (Guided Practice)
1. x = 38, y = 38
2. x = 25, y = 65
3. x = 70, y = 95
4. x = 120, y = 60
5. x = 65, y = 40
6. x = y = 70
7. x = 80, m  D = 20
8. x = 10, m  A = 55
Section 9.5 page 354
1. x = 30, y = 25, z = 15
2. x = 130, y = 120, z = 110
3. x = 110, y = 100, z = 100
4. x = 70, y = 110, z = 110
5. x = 50, y = 130, z = 65
6. x = 90, y = 90, z = 90
7. x = 104, y = 104, z = 52
8. x = 80, y = 40, z = 60
9. x = 50, y = 100, z = 35
Tangents, Arcs, and Chords
1. outside the circle
2. on the circle
3. inside the circle
4. chord
5. secant
6. tangent
7. 22.5
8. 3
9. arc RX or arc XS
10. arc XRS or arc RSX
11. 40
12. 330
13. 150
14. 160
15. 8
16. 10
17. 30
18. 80
19. 6 3
Pages 358 - 359: Cl. Ex. 1 – 9 all
1. 35
2. 40
3. 137.5
4. 80
5. 45
6. 40
1
7. 75 = (x + 100), x = 50
2
1
8. 30 = (x – 70), x = 130
2
1
9. 58 = (360 – x – x), x = 122
2
Section 9.6
1. 80
2. 100
3. 27.5
4. 117.5
5. 62.5
6. 35
7. 90
8. 62.5
Other Angles
1. 79
2. 64
3. 30
4. 54
5. 100
6. 84
7. 270
8. 40
9. 145
10. 10
11. 40
12. 45
13. 75
14. 50
15. 35
16. 40
17. 75
18. 35
19. 58
Circles and Lengths of Segments
1. 8
2. 13.5
3. 4 10
4. 4 3
5. 12
6. 2 2
7. 2
8. 16
3
9.
2
Angles and Segments
1. 35
2. 90
3. 70
4. 240
5. 65
6. 120
7. 100
8. 120
9. 50
10. 70
11. 35
12. 75
13. 60
14. 25
15. 30
16. 65
17. 15
18. 6
19. 6
20. 3
Circles
1. 90
2. 65
3. 30
4. 30
5. 75
6. 180
7. 105
8. 255
9. 4
10. 10
11. 35
12. 5 3
13. 68
14. 60
15. 7.2
16. x = 65, y = 115
17. 95
18. 70
19. 9 21
20. 14.5
Definitions for Unit Eleven: Applications of Circles
Section 7 – 6
117. arc length: a fraction of a circle’s circumference
Section 7 – 7
118. a region bounded by an arc of the cir le and the two radii to the arc’s endpoints
119. segment of a circle (drop-leaf): a part of a circle bounded by an arc and the segment
joining its endpoints
Section 7 – 8
120. geometric probability: a model in which points represent outcomes. Probabilities are
found by comparing measurements of sets of points.
Favorable outcomes
Possible outcomes
region
or
length of a favorable segment or
length of entire segment
area of favorable area
area of entire
Theorems for Unit Eleven: Applications of Circles
Section 11 – 5
120. An equations of a circle with center (h, k) and radius r is r2 = ( x – h )2 + ( y – k )2. This
equation is the standard form of the equation of a circle.
Section 7 – 6
121. The length of an arc of a circle is the product of the ratio measure of the arc and
360
the circumference of the circle.
Section 7 – 7
122. The area of a sector of a circle is the product of the ratio measure of the arc and
360
the area of the circle.
123. The area of segment of a circle is the area of the sector minus the area of the triangle
formed.
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 75
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 How is the equation of a circle written?
 How is the cente3r and radius of a circle found?
Objective(s): NCSCOS 2.03 Apply properties, definitions, and theorems of two-dimensional
figures to solve problems and write proofs: d) circles.
APK:
 Take up worksheet: Circles, Angles and Arcs
 Go over Test.
 Check Skills You’ll Need: page 615: 1 – 3 all (Find the length of the segment
and its midpoint)
 Go over.
TIP/SAP:
 Do together: worksheet labeled: The Distance Formula: 1 –4 all
 Derive the equation of a circle (using the distance formula)
 State, explain, and give examples of the standard form of the equation of a
circle.
 Examples: page 617: 1, 4, 7
 Students: page 617: 2, 5, 8
 Examples: page 617: 11, 13, 15
 Students: page 617: 10, 12, 14
 Discuss finding the coordinates of the center of a circle and the length of a
radius of a given equation in standard form.
 Examples: page 617: 17, 19 21
 Students; page 617: 16, 18 20
GP:

(with a partner) page 618: 27 – 37 odd
IP:

Worksheet labeled: The Distance Formula: 11 – 18 all; Go over
Assessment:
 Ticket Out the Door: page 619: 65 – 67 all
Homework:


Checkpoint Quiz 2: page 620: 1 – 10 all
Practice 11 – 5 (workbook, page 70)
The Distance Formula
Find the distance between the two points. If necessary, draw a graph, but you shouldn’t need to use
the distance formula.
1. (-3, 4) and (-3, -2) __________
2. (5. -5) and (5, 5) __________
3. (4, -2) and (-2, -2) __________
4. (0, 0) and (-4, 3) _________
Use the distance formula to find the distance between the points.
5. (7, 0) and (-2, 0) _________
6. (8, 10) and (2, 2) _________
7. (-1, 2) and (-4, 6) _________
8. (-3, 1) and (-1, 2) ________
9. (5, -4) and (0, 8) _________
10. (5, -5) and (-3, 5) _________
Find the center and the radius of each circle.
11. ( x – 1)2 + (y + 3)2 = 42
center __________
radius ___________
12. ( x + 2)2 + (y - 5)2 = 22
center __________ radius ___________
13. ( x + 1)2 + (y - 10)2 =
25
9
center __________ radius ___________
14. ( x + e)2 + (y - f)2 = 11
center __________ radius ___________
Write an equation of the circle described.
15. center (1, -2); radius 3
17. center (-2, 0); radius
16. center (-3, 4); radius 5
2
17. center (-1, 3); radius
1
3
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 76
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 How is sector area and arc length found?
Objective(s): NCSCOS 1.02 Use length, area, and volume of geometric figures to solve
problems. Include arc length and area of sectors of circles.
APK:
 Go over homework.
 Lesson Quiz 11 – 5 (page 619, TE)
 Go over.
TIP/SAP:
 Define arc length.
 State, explain, and give examples of finding arc length of a circle.
 Page 390: 35 – 39 odd
 Students; page 390: 34 – 38 even
 Define: sector of a circle and segment of a circle
 State, explain, and give examples of finding sector and segment area.
 Examples; page 398: 7 – 19 odd
 Students: page 398: 8 – 18 even
GP:



(with a partner) page 392: 61 – 65 all, 68
Page 398; 22 – 27 all
Go over.
IP:



Practice 7 – 6: 21 – 23 all (workbook, page 44)
Practice 7 – 7: 1 – 8 all (workbook, page 45)
Go over.
Assessment:
 Ticket Out the Door: Explain in your own words how to find arc length and
sector area.
Homework:
 Worksheet labeled: Arc Lengths and Area of Sectors
 Complete Practice 7 n- 7: 9 – 20 all (workbook, page 45)
Arc Lengths and Areas of Sectors
Leave answers in terms of .
1. In Circle O with radius 8, m AOB = 45. Find the length of arc AB and the area of sector
AOB.
Length of arc AB = ______________
A = ________________
2. In Circle O with diameter 14, m COD = 120. Find the length of arc CD and the area of
sector COD.
Length of arc CD = _____________
A = _____________
3. In Circle O with radius 12, m GOH = 30. Find the length of arc GH and the area of
sector GOH.
Length of arc GH = _______________ A = _______________
4. In Circle O with diameter 20, m EOF = 72. Find the length of arc EF and the area of
sector EOF.
Length of arc EF = ________________ A = _________________
5. The area of sector AOB is 20 and m AOB = 100. Find the radius of circle O.
6. The length of CD is 4.2 and m COD = 70. Find the radius of circle O.
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 77
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 How are segment and area models used to find the probabilities of events?
Objective(s): NCSCOS 1.03 Use length, area, and volume to model and solve problems
involving probability.
APK:
 Go over homework.
 Page 400: 41 – 46 all
 Go over.
TIP/SAP:
 Do together: Check Skills You’ll Need: page 402: 1 – 8 all
 State, explain, and give examples of a geometric probability.
 Examples: page 404: 1 – 7 odd
 Students: page 404: 2 – 6 even
 Examples: page 404: 8, 9
 Students: page 404: 10 – 13 all
 Examples; page 405: 23
 Students: page 405: 24, 25
GP:


(with a partner) Practice 7 – 8: 2 – 12 even (workbook, page 46)
Go over.
IP:


Practice 7 – 8: 1 – 11 odd
Go over.
Assessment:
 Practice 7 – 8: 13 – 16 all
 Go over.
Homework:


Page 406: 32 – 43 all
Page 407: 48 – 57 all
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 78
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 How are the applications in circles used?
Objective(s):
 NCSCOS 2.03 apply properties, definitions, and theorems of two-dimensional figures to
solve problems and write proofs: d) circles.
 NCSCOS 1.02 Use length, area, and volume of geometric figures to solve problems.
Include arc length and area of sectors of circles.
 NCSCOS 1.03 Use length, area, and volume to model and solve problems involving
probability.
APK:
 Go over homework.
 Review: equations of circles, sector area, segment area, arc length, and
geometric probability.
IP:

Major quiz on Sections 11 – 5, 7 – 6, 7 – 7. and 7 – 8 (45 minutes)
Homework:
 Cumulative Review chapters 1 – 9 (pages 81 – 82 of Assessment
Resources)
Unit Eleven Answers to Worksheets
The Distance Formula
1. 6
2. 10
3. 6
4. 5
5. 9
6. 10
7. 5
8. 5
9. 13
10. 8 2
11. center (1, -3), r = 4
12. center (-2, 5), r = 2
5
3
14. center (-e, f), r = 11
15. (x – 1)2 + (y + 2)2 = 9
16. (x + 3)2 + (y - 4)2 = 25
17. (x + 2)2 + y 2 = 2
1
18. (x + 1)2 + (y - 3)2 =
9
13. center (-1, 10), r =
Arc Lengths and Areas of Sectors
1. 2 , 8 
14
49
2.
,

3
3
3. 2 , 12 
4. 4 , 20 
5. 6 2
6. 10.8
Definitions for Unit Twelve: Solids
121.
prisms:
bases: congruent polygons lying in parallel planes
lateral faces: the faces of a prism that are not its bases
lateral edges: the parallel segments formed by adjacent lateral faces
altitude: a segment joining the two base planes and perpendicular to both
height: the length of the altitude of the prism
base edge: the parallel segments formed by an adjacent lateral face and a base
If s = the number of sides or number of base edges on one base then,
total number of edges = 3s
total number of faces = s + 2
total number of vertices = 2s
122.
right prism: a prism in which the lateral edges are perpendicular to the bases
123.
oblique prism: a prism in which the lateral edges are not perpendicular to the
bases
124.
lateral area: the sum of the areas of its lateral faces (L or L.A.)
125.
total area: the sum of the areas of all its faces (T or T. A.)
126.
pyramids:
vertex: the point of intersection of all the lateral edges
altitude: the segment from the vertex perpendicular to the base
height: the length of the altitude
lateral faces: the faces of the pyramids that are not a base. Lateral faces share the
vertex
of the pyramids and are triangular in shape
lateral edges: the segments formed by the intersection of adjacent lateral faces
slant height: the height of a lateral face
naming a pyramid: Name the vertex of the pyramid first, - then name the consecutive
vertices of the base
127.
regular pyramids: (four pyramids)
1. The base is a regular polygon.
2. All lateral edges are congruent.
3. All lateral faces are congruent isosceles triangles.
4. The altitude meets the base at its center.
128.
cylinder: a prism with a circular base
In a right cylinder, the segment joining the centers of the circular bases is an altitude.
The length of an altitude is called the height, h, of the cylinder. A radius of a base is
called a radius, r, of the cylinder.
129.
cone: a pyramid related solid with a circular base
The segment joining the vertex and the center of the base is the axis of the cone. If the
axis of the cone is perpendicular to the plane of the base, the cone is a right cone.
Otherwise the cone is oblique. The slant height of a right cone is the length of a
segment from the vertex to a point on the circle.
Theorems for Unit Twelve: Solids
124. The lateral area of a right prism equals the perimeter of a base times the height of the prism. ( L = ph )
125. The total area of a right prism equals the sum of the lateral area and the two base areas.
( T. A. = L. A. + 2B)
126. The volume of a right prism equals the area of a base times the height of a prism.
( V = Bh)
127. lateral area of a cylinder = (circumference of a base) (height); (C = 2 r)
128. total area of a cylinder = lateral area + 2 (base areas)
129. volume of a cylinder = (base area) (height)
130. lateral area of a pyramid =
1
(perimeter of the base)(height)
2
131. total area of a pyramid = lateral area + Base area
132. volume of a pyramid =
1
(Base area) (height)
3
133. lateral area of a cone =
1
(circumference) (slant height)
2
134. total area of a cone = lateral area + base area
135. volume of a cone =
1
(base area) (height)
3
136. area of a sphere = 4  r 2 or 4 (area of the Great Circle)
137. volume of a sphere =
4
r3
3
138. If the scale factor of two similar solids is a : b is:
1. The ratio of the perimeters, circumferences, heights, slant heights, lateral edges, apothems, base
edges, and radii is a : b.
2. The ratio of the base areas, lateral areas, and the total areas is a 2 : b2.
3. The ratio of the volumes is a 3 : b 3.
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 79
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 How are lateral area, total, and volume of prisms and cylinders
determined?
 How are prisms and cylinders related?
Objective(s):
 NCSCOS 1.02 Use length, area, and volume of geometric figures to solve problems.
 NCSCOS 2.04 Develop and apply properties of solids to solve problems.
APK:
 Take up Cumulative Review.
 Go over test.
TIP/SAP:
 Distribute definitions, theorems, and formulas for the solids unit.
 State, explain, and give examples of the parts of prisms and cylinders.
 Using gift-wrap and a box, demonstrate and describe lateral area, total
area, and volume.
 State and explain formulas used to calculate LA, TA and V of prisms and
cylinders. Tell the students NCDPI uses L for lateral area, and T for total
area on the EOC. Discuss cubes.
 Review formulas of areas of plane figures. These are used to find B, the
base area of the solid.
 Examples: page 532: 5 – 8 all
 Students: Practice 10 – 3: 1, 4, 7, 10, 13 (workbook, page 60)
 Examples: page 547: 1, 3, 5, 6, 7

GP:



Students: Practice 10 – 5: 1, 4, 7, 10 (workbook, page 62)
(with a partner) Practice 10 – 3: 2, 5, 8, 11, 14
Practice 10 – 5: 2, 5, 8, 11
Go over.
IP:



Practice 10 – 3: 3, 6, 9, 12, 15
Practice 10 – 5: 3, 9, 12
Go over.
Summarize:
 Ticket Out the Door: Explain the difference between LA, TA, and V.
Homework:
 Worksheet labeled: Prisms and Cylinders
 EOC Review Sheets
Prisms and Cylinders
1. Find the lateral area, total area, and volume of a rectangular solid with length 7 cm,
width 6 cm, and height 2 cm.
L.A. = __________, T.A. = __________, V = __________
2. Find the total area and volume of a cube with edge 5 cm.
T.A. = _________, V = _________
3. Find the lateral area of a right hexagonal prism with height 12 and base edges 3, 4, 5, 6,
5.2, and 6.3. _________
4. The total area of a cube is 216 cm2. Find the length of an edge. ________
5. The base of a right prism is a square with edge 4 cm. The volume is 64 cm 3. Find the
height. _________
6. Find the lateral area, total area, and volume of a triangular prism base edges 6, 8, 10 and
height 12.
L.A. = ________, T.A. = _________, V = ___________
7. Find the lateral area, total area, and volume of a prism with an equilateral triangular
base with side 6 and height 8.
L.A. = _________, T.A. = _________. V = _________
8. Find the lateral area, total area, and volume of a cylinder with radius 6 and height 8.
L.A. = _________, T.A. = __________, V = ___________
9. The volume of a cylinder is 81. If r = 3, find h. ___________
10. The volume of a cylinder is 36. If h = 4, find the lateral area. __________
11. The lateral area of a cylinder is 100. If r = 5, find h. __________
12. The total area of a cylinder is 144. If r = h, find r. __________
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 80
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 How are lateral area, total area, and volume of pyramids and cones
determined?
 How are pyramids and cones related?
Objective(s):
 NCSCOS 1.02 Use length, area, and volume of geometric figures to solve problems.
 NCSCOS 2.04 Develop and apply properties of solids to solve problems.
APK:




Take up EOC Review Sheets.
Go over homework.
Standardized Test Prep: page 534: 38 – 40 all; page 550: 40, 21
Go over.
TIP/SAP:
 State, explain, and give examples of parts of pyramids and cones.
 Show how rectangles, circles, and semicircles are used to form pyramids
and cones.
 State and explain formulas used to calculate LA< TA, and V of pyramids
and cones.
 Examples: page 540 – 541: 1, 4, 7, 13, 15, 18, 26
 Students: pages 540 – 541: 3, 5, 9, 13, 16, 19, 27
 Examples: page 554: 5, 9, 13
 Students: page 554: 7, 10
GP:



(with a partner) Practice 10 – 4; 1, 4, 7, 10
Practice 10 – 6: 4, 7, 10, 13
Go over.
IP:



Practice 10 – 4: 2, 5, 9, 12
Practice 10 – 6: 2, 8, 11, 14
Go over.
Summarize:
 Ticket Out the Door: explain the ratio of volume of cylinders and cones that
have equal heights and radii.
Homework:
 Worksheet labeled: Pyramids and Cones
 EOC Review Sheets.
Pyramids and Cones
1. A regular triangular pyramid has base edges 6 cm, 6 cm, and 6 cm and slant height 10
cm. Find its lateral area. __________
2. Find the volume of a hexagonal pyramid with base edge 8 cm and height 12 cm.
_________
3. Find the lateral area, total area, and volume of a square pyramid whose base edge is 9
and height is 6.
L.A. = __________, T.A. = __________, V = __________
4. Find the lateral area, total area, and volume of a square pyramid whose height is 15 and
slant height is 25.
L.A. = __________, T.A. = __________, V = ___________
5. Find the lateral area, total area, and volume of a cone whose radius is 3 and slant height
is 10.
L.A. = __________, T.A. = ___________, V = ___________
6. Find the lateral area, total area, and volume of a cone where r = 7 and h = 24.
L.A. = __________, T.A. = ___________, V = ___________
7. A cone has radius 6 and slant height 19. Find the height, lateral area, total area, and
volume.
h = __________, L.A. = ___________, T.A. = ___________, V = ___________
8. A cone has radius 5 and volume 100. Find the height, slant height, lateral area, and
total area.
h = __________, l = __________, L.A. = _________, T.A. = ___________
9. The lateral area of a cone is 32 and the slant height is 8. Find the radius, height, total
area, and volume.
r = __________, h = ___________, T.A. = ____________, V = ____________
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 81
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 How are surface area and volume of a sphere found?
 How is the “Great Circle” related to the surface area?
Objective(s):
 NCSCOS 1.02 Use length, area, and volume of geometric figures to solve problems.
 NCSCOS 2.04 Develop and apply properties of solids to solve problems.
APK:




Take up EOC Review Sheets.
Go over homework.
Standardized Test Prep: page 543: 55 – 58 all; pages 556 – 557: 37 – 41 all
Go over.
TIP/SAP:
 Discuss formulas for spheres.
 Examples: pages 560 – 561: 1, 2, 12
 Students: Worksheet labeled: Spheres Classwork Examples
GP:


(with a partner) complete the Guided Practice on the Spheres Classwork
worksheet.
Go over.


Practice 10 – 7: 1, 3, 7, 9, 11, 13
Go over.
IP:
Summarize:

Ticket Out the Door: Explain what the “Great Circle” is.
Homework:
 Worksheet labeled: Spheres homework
 EOC Review Sheets
Spheres Classwork
Examples:
1. Find the area and volume of sphere with radius 3.
A = ___________
V = ____________
2. Find the area and volume of a sphere with radius
A = ___________
V = _____________
3. Find the area and volume of a sphere with radius
A = ___________
1
.
3
3.
V = _____________
4. Find the radius and volume of a sphere whose area is 576.
r = __________
V = ___________
5. Find the radius and area of a sphere whose volume is
r = __________
1372
.
3
V = ____________
Guided Practice:

. Find its diameter. _____________
4
7. The area of a sphere is 9. Find it s volume. ___________
6. The area of a sphere is
8. A plane passes 5 cm from the center of a sphere with radius 3 cm. Find the area of the
circle of intersection. __________
9. When a plane passes 5 cm from the center of a sphere, the radius of the circle of
intersection is 12 cm. Find the volume of the sphere. __________
10. A scoop of ice cream with radius 4 cm is placed on an ice-cream cone with radius 3 cm
and height 15 cm. Is the cone big enough to hold the ice cream if it melts? Justify your
answer.
11. A spherical fishbowl has diameter 24 cm. To fill the fishbowl three-fourths full, about
how many liters of water will you need? Give you answer to the nearest 0.1 L. Use  =
3.14. (1000 cm3 = 1 L)
Spheres Homework
1. Find the area and volume of a sphere with radius 9.
A = ___________
V = _____________
2. Find the radius and volume of a sphere with area 200.
r = ___________
V = _____________
3. Find the radius and area of a sphere with volume 288.
r = ___________
A = ___________
4. Find the area and volume of a sphere with radius
A = __________
1
.
4
V = ___________
5. Find the area of the circle formed when a plane passes 4 cm from the center of a sphere
with radius 10 cm. ___________
6. Find the area of the circle formed when a plane passes 5 cm from the center of a sphere
with radius 12 cm. ___________
7. A water storage tank consists of a cylinder capped with a hemisphere. Find the volume
of the tank. __________
8. Find the volume of a sphere with area 36. ____________
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 82
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 How is the ratio of the perimeters, areas, and volumes of similar geometric
figures determined?
Objective(s):
 NCSCOS 1.02 Use length, area, and volume of geometric figures to solve problems.
 NCSCOS 2.04 Develop and apply properties of solids to solve problems.
APK:




Take up EOC Review Sheets.
Go over homework.
Standardized Test Prep: page 563: 52 – 59 all
Go over.
TIP/SAP:
 Review similar triangles and scale factor.
 Compare similar and congruent solids.
 State, explain, and give examples of theorem for ratios of similar solids and
parts.
 Examples: page 568 – 569: 1 – 11 all
 Students: Practice 10 – 8: 1 – 13 odd
GP:



(with a partner): practice 10 – 8: 2 – 14 even
Go over.
Make models of polyhedra using toothpicks and gumdrops.
IP:


Worksheet labeled: Areas and Volumes of Similar Solids Classwork
Go over.
Assessment:
 Standardized Test Prep: page 571: 38 – 42 all
 Go over.
Homework:
 Worksheet labeled: Areas and Volumes of similar Solids Homework
 Worksheet labeled; Ratios of Areas
 EOC Review Sheets
Areas and Volumes of Similar Solids
Are the given solids similar?
1. Two regular square pyramids have heights 10 and 12. The bases are squares with sides
4 and 4.9, respectively.
2. One rectangular solid has length 7, width 5, and height 3. Another rectangular solid has
length 14, width 10, and height 9.
3. Two right triangular prisms have heights 4 and 6. Their bases are triangles with sides 3,
4, 5, and 6, 8, 10, respectively.
Complete the table, which refers to two similar prisms.
Scale factor
Ratio of base perimeters
Ratio of heights
Ratio of lateral areas
Ratio of total areas
Ratio of volumes
4.
2:5
5.
6.
7.
8.
1:3
4:49
125:216 27:1000
9. Two similar cones have volumes 27 and 64. Find the ratio of:
a. the radii
b. the slant heights
c. the lateral areas
10. Two spheres have radii 5 cm and 7 cm. Find the ratio of:
a. the areas
b. the volumes
11. Two foam plastic balls have scale factor 1:3.
a. If the smaller b all has radius 6 cm, what is the radius of the larger ball?
b. If the area of the larger ball is 36 cm2, what is the area of the smaller ball?
c. If the larger ball weighs 12 g. about how much does the smaller ball weigh?
(Hint: Weight is related to volume.)
Areas and Volumes of Similar Solids
1. Two cones have radii 8 and 12. The heights are 20 and 30. Are the cones similar?
2. Two cylinders have radii 10 and 25. Their heights are 36 and 90. Are the cylinders
similar?
3. Two cones have radii 16 and 48. The heights are 32 and 144. Are the cones similar?
4. Their heights of two right prisms are 9 and 15. The bases are squares with sides 27 and
45. Are the prisms similar?
Find the indicated ratios (in simplest form) for the given solids.
5. Two similar cylinders with radii 5 and 8.
a. heights _________
b. total areas _________ c. volumes _________
6. Two similar cones with volumes 8 and 64.
a. radii _________
b. slant heights __________
c. lateral areas __________
7. Two similar cylinders with lateral areas 36and 81.
a. heights _________
b. total areas __________
c. volumes __________
8. Two similar pyramids with heights 3 and 5.
a. base areas _________ b. total areas ________ c. volumes _________
9. Two similar cones with volumes 27and 125.
a. heights ________
b. base areas _________ c. total areas _________
10. Two spheres with radii 4 cm and 10 cm.
a. areas __________
b. volumes _________
11. Two spheres with diameters 18 and 24.
a. areas __________
b. volumes ________
12. Two similar pyramids with volumes 24 and 648.
a. heights _________
b. base areas __________
c. total areas _________
Ratios of Areas
Complete.
1. The ratio of the perimeters of two similar triangles is 3:5. The scale factor is ________
and the ratio of their areas is ________.
2. The ratio of the areas of two similar rectangles is 25:36. The scales factor is _______
and the ratio of their perimeters is __________.
3. The ratio of the areas of two squares is 16:36. The scale factor is _________ and the
ratio of their perimeters is __________.
4. Two circles have radii 5 and 7. The ratio of their areas is _________.
5. RST and XYZ are similar triangles with RS = 8 and XY = 12. The ratio of their
perimeters is ________ and the ratio of their areas is __________.
6. The areas of two circles are 144 and 64. The ratio of their circumferences is
_________.
7. Two similar polygons have scale factor 3:5. The area of the larger polygon is 125. The
area of the smaller polygon is _________.
Geometry Lesson Plans for Block Schedule
Aligned to NCSCOS –2003
(Learning-Focused/Reading in the Content Area)
Day: 83
Date: ________________________________ Block(s): 1 2 3 4
Essential Question(s):
 How are LA, TA, and V of solids found?
Objective(s):
 NCSCOS 1.02 Use length, area, and volume of geometric figures to solve problems.
 NCSCOS 2.04 Develop and apply properties of solids to solve problems.
TIP/SAP/GP:
 Using the models, complete the “Bubbles and the Geometry Connection”
activity.
IP:

Test on Unit 12. (Finish for homework if not finished in class. Students
may use their Theorem sheet for the formulas.)
Homework:
 EOC Review Sheets.
Q. E. D.
Bubbles and the Geometry Connection
Recipe for the bubble solution:
1 gallon of water
1 cup of Dawn dishwashing detergent
2 tsp. of Glycerin
Materials:
pipe cleaners
bubble solution
a container large enough for dipping the models
newspaper
Geometry Connections:
faces
angles
edges
patterns
vertices
surfaces
platonic solids
compare linear, two-dimensional and three-dimensional objects
Background Information:
Patterns created by the bubble solution might be expected to form around the sides.
Instead, the bubble solution would meet near the center, sometimes forming another
geometric shape. This is an illustration of the principles of surface tension. The elastic,
rubbery skin formed by the attraction of molecules to each other is pulling itself into the
smallest area possible.
A second discovery can be made regarding the pattern relationship between vertices,
edges, and faces. Euler’s Theorem states that “vertices + faces = edges + 2”.
What the students will do:
1. Build the shapes indicated on the worksheet using pipe cleaners.
2. Complete the chart.
3. Make observations while dipping the two-dimensional shapes into the mixture.
4. Predict what will happen when the three-dimensional shapes are dipped.
5. Tie a string to the shapes and dip the shapes into the bubble mixture.
6. Record observations after shapes have been dipped (possibly more than once).
Discussion:
1. Is the pattern the same each time?
2. How could you change the pattern?
3. Find a relationship between the vertices, edges, and faces.
4. How could you make the bubbles last longer?
Bubbles and the Geometry Connection Chart
Name of Shape
triangle
square
tetrahedron
square pyramid
triangular prism
cube
hexagonal prism
Sketch of
Shape
Number
of
vertices
Number
of lateral
edges
Number
of base
edges
Total
number
of edges
Shape of
lateral
faces
Number
of lateral
faces
Total
number
of faces
Unit Test
Name _________________________
Unit: Polyhedra
Date __________________________
Directions: Write the formula used. Show all work.
1. A right rectangular prism has length 8, width 4, and height 5. Find:
a. total area
b. volume
2. A right trapezoidal prism has a base perimeter 22 cm, base area 24 cm 2,
and height 10 cm. Find:
a. lateral area
b. volume
3. The total area of a cube is 150 cm2. Find:
a. length of an edge
b. volume
4. A regular square pyramid has a base edge 6 and height 4. Find:
a. slant height
b. length of a lateral edge
c. lateral area
d. volume
In questions 5 – 7, leave your answers in terms of  when appropriate.
5. The radius of a cylinder is 6 and height is 2. Find:
a. lateral area
b. volume
6. The volume of a cylinder is 125 and the radius is equal to the height. Find
the lateral area.
7. The radius of a cone is 3 and the height is 9. Find:
a. slant height
b. lateral area
c.volume
8. If the radius of a cone is multiplied by 3 and the height remains the same,
then the volume is multiplied by _________.
For questions 9 -12, leave your answers in terms of  when appropriate.
9. The radius of a sphere is 10. Find:
a. area
b. volume
10. The volume of a hemisphere is 144. Find the radius.
11. Two similar pyramids have heights 9 and 12. Find the ratio of the:
a. lateral areas
b. volumes
12. Two similar cones have volumes 24 and 81. If the lateral area of the
smaller is 32, find the lateral area of the larger cone.
Bonus (Optional)
A cylindrical water tank with radius 2 feet and length 6 feet is filled with water to a
depth of 3 feet when in horizontal position. If the tank is turned upright, what is
the depth of the water? Give you answers in terms of .
Unit Twelve Answers to Worksheets
Prisms and Cylinders
1. L = 52 cm2, T = 136 cm2, V = 84 cm3
2. L = 4.2 m2, T = 11.4 m2, V = 1.8 m3
3. T = 150 cm2, V = 125 cm3
4. 6 cm
5. 4 cm
6. L = 288, T = 336, V = 288
7. L = 144, T = 144 + 18 3 , V = 72 3
8. L = 96 , T = 168 , V = 288 
9. 9
10. 24 
11. 10
12. 6
Pyramids and Cones
1. 90 cm2
2. 384 3 cm2
3. L = 135, T = 216, V = 162
4. L = 2000, T = 3600, V = 8000
5. L = 30 , T = 39, V = 3  91
6. L = 175 , T = 224 , V = 392 
7. h = 8, L = 60 , T = 96 , V = 96 
8. h = 12, l = 13, L = 65 , T = 90 
64 3
9. r = 4, h = 4 3 , T = 48 , V =

3
Spheres
1. A = 36 , V = 36 
4
4
2. A =
, V =

9
81
3. A = 12 , V = 4  3
4. r = 12, V = 2304 
5. r = 7, A = 196 
1
6.
2
9
7.

2
8. not possible
8788
9.
 cm2
3
10. No, the volume of the cone is 45  cm3, and the volume of the ice cream is
256
 cm3.
3
11. 5.4 L
Spheres Homework
1. A = 324 , V = 972 
1000
2. r = 5 2 , V =

3
3. r = 6, A = 144 
1
1
4. A =
, V =

4
48
5. 84  cm2
6. 119  cm2
7. 126  m3
8. 36 
2
Areas and Volumes of Similar Solids
1. yes
2. no
3. no
4.
2:5
2:5
4:25
4:25
8:125
5.
1:3
1:3
1:9
1:9
1:27
6.
2:7
2:7
2:7
4:49
8:343
9. a) 3:4, b) 3:4, c) 9:16
10. a) 25:49, b) 125: 343
11. a) 9 cm, b) 16  cm2, c) about 3.6 g
Areas and Volumes of Solids
1. yes
2. yes
3. no
4. yes
5. a) 5:8, b) 25:64, c) 125: 512
6. a) 1:2, b) 1:2, c) 1:4
7. a) 2:3, b) 4:9, c) 8:27
8. a) 9:25, b) 9:25, c) 27:125
9. 3:4, b) 9:16, c) 9:16
7.
5:6
5:6
5:6
25:36
25:36
8.
3:10
3:10
3:10
9:100
9:100
10. a) 4:25, b) 8:125
11. a) 9:16, b) 27:64
12. a) 1:3, b) 1:9, c) 1:9
Ratio of Areas
1. 3:5, 9:25
2. 5:6, 5:6
3. 2:3, 2:3
4. 25:49
5. 2:3, 4:9
6. 3:2
7. 45
Unit Test
1. a) 184, b) 160
2. a) 220 cm2, b) 240 cm3
3. a) 5 cm, b) 125 cm3
4. a) 5, b) 34 , c)60, d) 48
5. a) 24, b) 72 
6. 50 
7. a) 3 10 , b) 9  10 , c) 27 
8. 9
4000
9. a) 400 , b)

3
10. 6
11. a) 9:16, b) 27:64
12. 72 
Bonus: 4 +
3 3
2