Geo H - Chapter 11 Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. A circle has a circumference of 50 meters. Find its diameter.
a. 12.5 m
c. 7.96 m
b. 15.92 m
d. 25 m
2. Write an expression for the circumference of a circle with diameter d is.
a.
c.
b.
d.
3. For a circle of radius 5 feet, find the length of an arc s with a measure of 28°.
a.
c.
7
1
9
36
b.
d.
140
7
18
4. Find the length of a 40° arc in a circle with a radius of 4.
a.
c.
b.
d.
5. An automobile has 20-inch diameter wheels. If the wheels revolved three times after the brakes were applied, the
stopping distance was approximately _____.
a. 15.7 ft
c. 157 ft
b. 7.85 ft
d. 26.2 ft
6. A park has a circular swimming pool. The diameter of the pool is 19 ft. What is the distance traveled if you swim
around the edge of the pool once?
a. 38 ft
c. 119.38 ft
b. 59.66 ft
d. 179.07 ft
7. Find the area of the shaded region.
a.
b.
College Entrance Exam:
c.
d.
8. The figure below represents an oval track. The rounded portions of the track are semicircles. What is the length of
the track?
12 ft
12 ft
106 ft
a.
b.
c.
d.
9. Write an expression for the area of a circle with diameter d.
a.
b.
c.
d.
10. In this figure, each circle has a radius of 2 inches. What is the area of the portion outside the circles but inside the
square? Express your answer in terms of .
a.
b.
c.
11. Find the area of an equilateral triangle with side length 14.
a.
b. 42
c. 98
d.
d.
12. Find the area of a regular octagon with side length 9 cm.
a. 782.2
c. 423.3
b. 391.1
d. 374.4
13. Find the area of a regular decagon with radius 7 cm. Round to the nearest tenth.
a. 162.6
c. 233.0
b. 144.0
d. 288.0
14. A regular hexagon has an apothem of 2 and a side length of
. Its area is _____.
a.
c.
b.
d.
15. What is the perimeter of the regular hexagon to the nearest inch?
a.
b.
c.
d.
12 inches
24 inches
41 inches
48 inches
16. Find the number of vertices, faces, and edges for the figure below.
a.
b.
c.
d.
6 vertices, 6 faces, 10 edges
5 vertices, 6 faces, 10 edges
7 vertices, 7 faces, 11 edges
10 vertices, 6 faces, 6 edges
17. Describe the cross section.
a. hexagon
c. rectangle
b. pyramid
d. triangle
18. According to Euler's Theorem, the number of faces (F), vertices (V), and edges (E) of a polyhedron is related by
the formula _____.
a. F + V = E + 2
c. F + E = V + 2
b. E + V = F + 2
d. F + V = E – 2
19. An aquarium in a restaurant is a rectangular prism and measures 4.5 feet by 4 feet by 2 feet. What is the volume of
the aquarium?
a. 32 cubic feet
c. 10.5 cubic feet
b. 36 cubic feet
d. 12.5 cubic feet
20. Find the exact volume of a cylinder that has a height of 18 inches and a radius of 8 inches.
a. 384
c.
b.
d.
21. Find the volume of the right triangular prism.
a. 210
b. 31
c. 105
d. 20.5
22. The volume of the right prism is _____.
a.
b.
c. 120
d. 60
23. The volume of the right circular cylinder is about _____.
a. 265.5
b. 326.7
c. 1036.9
d. 1061.9
24. The pyramid shown has a rectangular base and faces that are isosceles triangles. Find its volume.
5 ft
6 ft
8 ft
a. 80
b. 240
c. 34
d. 384
25. Calculate the volume of the cone. Use
a.
b.
c.
d.
26.17
50
157
471
26. A pyramid-shaped puzzle exactly fits its cubic storage box. The space between the puzzle and the sides of the box
is filled with a light-weight plastic foam to help protect the puzzle during shipping.
What is the volume of the foam?
a. 171.50
b. 228.67
c. 240.10
d. 114.33
27. Find the surface area of a sphere that has a diameter of 16 cm. Express your answer in terms of .
a. 256
c. 1024
b. 64
d. 2048

3
28. The top of the cylindrical container shown has the shape of a hemisphere. The total volume of the container is
_____.
a.
b.
c.
d.
Numeric Response
29. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet.
The circle graph below shows the main sources of water pollution in a county.
What is the measure, in degrees, of the central angle of the section of the circle that represents the pollution caused
by industry?
30. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet.
How many edges of a square pyramid are NOT parallel to any other edges?
31. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet.
The shaded area in the figure is a planar cross section of a cylindrical metal drum which has had the lid welded
closed. Edith will cut the drum open along the edges of the cross section and add a base containing legs to make a
barbecue. (The figure may not be drawn to scale.)
After the drum is cut open, the cut edges must be ground to make the edges smooth. Along how many inches of
metal edge must Edith grind?
Short Answer
32. Find the area of the shaded region. (Assume that the ends of the figure are semicircles.)
33. A square is inscribed in a circle of radius
. Find the area of the square.
34. A student is determining the details of a circle graph showing the results of the election for president of the student
government.
If 490 students voted, how many voted for Meyer? Round your answer to the nearest whole number.
35. Find the probability that a point chosen at random on
is on
.
36. Find the probability that a point chosen at random on
is on
.
37. A trivia game has four categories of questions. The questions are on cards colored red, blue, green, and yellow.
There are a different number of questions in each category, so the game spinner that determines a player's category
is divided into sectors proportional to the number of cards of each color, as shown on the spinner below. If the
cards in a category are all used, then a player spinning that color loses a turn.
On the first spin of the game, what is the probability that a player will be assigned a question from the blue
category? Give your answer as a decimal rounded to the nearest hundredth.
38. Use Euler's Theorem to calculate how many faces a polyhedron has if it has 30 edges and 12 vertices.
39. The base of a pyramid is a regular pentagon and each of its other faces is an equilateral triangle.
a. How many faces does the pyramid have?
b. How many edges does the pyramid have?
c. How many vertices does the pyramid have?
40. The base of a pyramid is a regular hexagon and each of its other faces is an isosceles triangle with base angles
measuring 70°.
a. How many faces does the pyramid have?
b. How many edges does the pyramid have?
c. How many vertices does the pyramid have?
41. Find the volume of the rectangular prism.
42. Find the volume of the right prism.
43. Find the volume of the cylinder. (Round the result to one decimal place.)
44. Find the surface area and volume of the cylinder that can be folded from the net shown.
45. Find the volume of the oblique prism.
46. Find the volume of the right cone. Round your answer to two decimal places.
47. Find the diameter of a sphere that has a surface area of
.
48. The areas of corresponding faces of two similar triangular prisms are
and
What is the ratio of the
corresponding side lengths? of the perimeters of the corresponding faces? of the volumes?
49. The surface area of a sphere is 200
. If the radius were three times as large, what would the surface area be?
50. The surface areas of two similar solids are
is the volume of the smaller one?
and
The volume of the larger one is
What
Geo H - Chapter 11 Review
Answer Section
MULTIPLE CHOICE
1. ANS:
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14. ANS:
B
PTS: 1
DIF: Level B
Lesson 11.1 Circumference and Arc Length
DOK 2
NOT: 978-0-547-31534-8
C
PTS: 1
DIF: Level A
Lesson 11.1 Circumference and Arc Length
DOK 2
NOT: 978-0-547-31534-8
A
PTS: 1
DIF: Level A
Lesson 11.1 Circumference and Arc Length
DOK 2
NOT: 978-0-547-31534-8
A
PTS: 1
DIF: Level A
Lesson 11.1 Circumference and Arc Length
DOK 2
NOT: 978-0-547-31534-8
A
PTS: 1
DIF: Level B
Lesson 11.1 Circumference and Arc Length
DOK 2
NOT: 978-0-547-31534-8
B
PTS: 1
DIF: Level B
Lesson 11.1 Circumference and Arc Length
DOK 2
NOT: 978-0-547-31534-8
B
PTS: 1
DIF: Level A
NCTM.PSSM.00.MTH.9-12.MEA.2.b
Lesson 11.1 Circumference and Arc Length
DOK 2
NOT: 978-0-547-31534-8
D
PTS: 1
DIF: Level B
Lesson 11.1 Circumference and Arc Length
DOK 2
NOT: 978-0-547-31534-8
D
PTS: 1
DIF: Level A
NCTM.PSSM.00.MTH.9-12.MEA.2.b
formula | circle | diameter | area
MSC: DOK 2
D
PTS: 1
DIF: Level B
NCTM.PSSM.00.MTH.9-12.MEA.2.b
square | circle | area
MSC: DOK 2
D
PTS: 1
DIF: Level A
NCTM.PSSM.00.MTH.9-12.MEA.2.b
area | triangle | equilateral
MSC: DOK 2
B
PTS: 1
DIF: Level B
NCTM.PSSM.00.MTH.9-12.MEA.2.b
area | polygon | trigonometry | regular
978-0-547-31534-8
B
PTS: 1
DIF: Level B
NCTM.PSSM.00.MTH.9-12.MEA.2.b
area | polygon | trigonometry | regular
978-0-547-31534-8
A
PTS: 1
DIF: Level B
REF: MHGM0102
KEY: circle | diameter | radius | circumference
REF: HLGM1090
KEY: circle | diameter | circumference
REF: MGEO0025
KEY: circle | radius | arc length
REF: MLGE0268
KEY: radius | length | arc
REF: HLGM1092
KEY: distance | circle | diameter | revolution
REF: MLGE0271
KEY: word | diameter | circumference
REF: MLA20277
KEY: circle | area | sector
REF: MIM10719
KEY: word | perimeter
REF:
TOP:
NOT:
REF:
TOP:
NOT:
REF:
TOP:
NOT:
REF:
TOP:
MSC:
HLGM1100
Lesson 11.2 Areas of Circles and Sectors
978-0-547-31534-8
MGEO0032
Lesson 11.2 Areas of Circles and Sectors
978-0-547-31534-8
OTGS0035
Lesson 11.3 Areas of Regular Polygons
978-0-547-31534-8
PHGM1119
Lesson 11.3 Areas of Regular Polygons
DOK 2
REF: PHGM1121
TOP: Lesson 11.3 Areas of Regular Polygons
MSC: DOK 2
REF: MLGE0262
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
LOC:
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ANS:
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TOP:
KEY:
NOT:
NCTM.PSSM.00.MTH.9-12.MEA.2.b
TOP: Lesson 11.3 Areas of Regular Polygons
area | regular | hexagon | apothem MSC: DOK 2
NOT: 978-0-547-31534-8
B
PTS: 1
DIF: Level B
62aaf0d0-4f27-11db-b4d8-0011258082f7
TOP: Lesson 11.3 Areas of Regular Polygons
perimeter of a regular polygon | regular polygon
MSC: DOK 2
978-0-547-31534-8
A
PTS: 1
DIF: Level A
REF: MOT80315
Lesson 11.5 Explore Solids
KEY: vertices | edges | faces
DOK 2
NOT: 978-0-547-31534-8
D
PTS: 1
DIF: Level B
REF: MGEO0034
NT.CCSS.MTH.10.9-12.G.GMD.4
NCTM.PSSM.00.MTH.9-12.GEO.4.b | NCTM.PSSM.00.MTH.9-12.MEA.2.c
Lesson 11.5 Explore Solids
KEY: plane | three-dimension | cross-section
DOK 2
NOT: 978-0-547-31534-8
A
PTS: 1
DIF: Level A
REF: HLGM1136
Lesson 11.5 Explore Solids
KEY: Euler's Theorem | vertices | faces | edges
DOK 2
NOT: 978-0-547-31534-8
B
PTS: 1
DIF: Level B
REF: TASH0033
NCTM.PSSM.00.MTH.9-12.MEA.2.b | NCTM.PSSM.00.MTH.9-12.PRS.2
Lesson 11.6 Volume of Prisms and Cylinders
KEY: volume | rectangular | solid | prism | box
DOK 2
NOT: 978-0-547-31534-8
C
PTS: 1
DIF: Level B
REF: MLGE0453
NT.CCSS.MTH.10.9-12.G.GMD.3
LOC: NCTM.PSSM.00.MTH.9-12.MEA.2.b
Lesson 11.6 Volume of Prisms and Cylinders
KEY: radius | surface area | cone | height
DOK 2
NOT: 978-0-547-31534-8
C
PTS: 1
DIF: Level B
REF: MLGE0318
NCTM.PSSM.00.MTH.9-12.MEA.2.b
Lesson 11.6 Volume of Prisms and Cylinders
KEY: volume | prism
DOK 2
NOT: 978-0-547-31534-8
D
PTS: 1
DIF: Level B
REF: HLGM1171
NCTM.PSSM.00.MTH.9-12.MEA.2.b
Lesson 11.6 Volume of Prisms and Cylinders
KEY: right | volume | prism
DOK 2
NOT: 978-0-547-31534-8
D
PTS: 1
DIF: Level B
REF: HLGM1172
NT.CCSS.MTH.10.9-12.G.GMD.3
LOC: NCTM.PSSM.00.MTH.9-12.MEA.2.b
Lesson 11.6 Volume of Prisms and Cylinders
KEY: right | volume | cylinder | circular
DOK 2
NOT: 978-0-547-31534-8
A
PTS: 1
DIF: Level B
REF: MHGM0097
NT.CCSS.MTH.10.9-12.G.GMD.3
LOC: NCTM.PSSM.00.MTH.9-12.MEA.2.b
Lesson 11.7 Volumes of Pyramids and Cones
KEY: square | volume | pyramid
DOK 2
NOT: 978-0-547-31534-8
C
PTS: 1
DIF: Level A
REF: MLGE0320
NT.CCSS.MTH.10.9-12.G.GMD.3
LOC: NCTM.PSSM.00.MTH.9-12.MEA.2.b
Lesson 11.7 Volumes of Pyramids and Cones
KEY: volume | cone
DOK 2
NOT: 978-0-547-31534-8
B
PTS: 1
DIF: Level B
REF: MC100077
NT.CCSS.MTH.10.9-12.G.GMD.3
LOC: NCTM.PSSM.00.MTH.9-12.MEA.2.b
Lesson 11.7 Volumes of Pyramids and Cones
word | composite | real-life | volume | cube | pyramid
MSC: DOK 2
978-0-547-31534-8
27. ANS:
LOC:
TOP:
MSC:
28. ANS:
NAT:
TOP:
MSC:
A
PTS: 1
DIF: Level B
NCTM.PSSM.00.MTH.9-12.MEA.2.b
Lesson 11.8 Surface Area and Volume of Spheres
DOK 2
NOT: 978-0-547-31534-8
B
PTS: 1
DIF: Level B
NT.CCSS.MTH.10.9-12.G.GMD.3
Lesson 11.8 Surface Area and Volume of Spheres
DOK 2
NOT: 978-0-547-31534-8
REF: GGEM0029
KEY: diameter | sphere | surface area
REF: HLGM1197
LOC: NCTM.PSSM.00.MTH.9-12.MEA.2.b
KEY: volume | cylinder | hemisphere
NUMERIC RESPONSE
29. ANS: 144
PTS:
TOP:
MSC:
30. ANS:
1
DIF: Level A
REF: MC100095
Lesson 11.2 Areas of Circles and Sectors
DOK 2
NOT: 978-0-547-31534-8
4
LOC: NCTM.PSSM.00.MTH.9-12.REP.1
KEY: solve | word | data | graph | pie chart
PTS:
TOP:
MSC:
31. ANS:
1
DIF: Level B
REF: MC100121 LOC: NCTM.PSSM.00.MTH.9-12.REP.1
Lesson 11.5 Explore Solids
KEY: square | pyramid | edges
DOK 2
NOT: 978-0-547-31534-8
132
PTS: 1
DIF: Level B
REF: MC100150 LOC: NCTM.PSSM.00.MTH.9-12.REP.1
TOP: Lesson 11.5 Explore Solids
KEY: word | perimeter | real-life | cylinder | cross-section
MSC: DOK 2
NOT: 978-0-547-31534-8
SHORT ANSWER
32. ANS:
PTS: 1
DIF: Level B
REF: MGEO0033
TOP: Lesson 11.2 Areas of Circles and Sectors
MSC: DOK 2
NOT: 978-0-547-31534-8
33. ANS:
36 sq. units
PTS:
LOC:
TOP:
MSC:
34. ANS:
253
LOC: NCTM.PSSM.00.MTH.9-12.MEA.2.b
KEY: area | rectangle | difference | semicircle
1
DIF: Level C
REF: MLGE0284
NCTM.PSSM.00.MTH.9-12.MEA.2.b | NCTM.PSSM.00.MTH.9-12.MEA.2.c
Lesson 11.2 Areas of Circles and Sectors
KEY: inscribed square | area
DOK 2
NOT: 978-0-547-31534-8
PTS: 1
DIF: Level B
REF: MC100111
KEY: word | angle | real-life | sum | circle graph | pie chart
NOT: 978-0-547-31534-8
35. ANS:
TOP: Lesson 11.2 Areas of Circles and Sectors
MSC: DOK 2
PTS: 1
DIF: Level A
KEY: line | geometric | probability
36. ANS:
REF: MLGE0431
MSC: DOK 2
TOP: Lesson 11.4 Use Geometric Probability
NOT: 978-0-547-31534-8
PTS: 1
DIF: Level B
KEY: line | geometric | probability
37. ANS:
0.21
REF: MLGE0432
MSC: DOK 2
TOP: Lesson 11.4 Use Geometric Probability
NOT: 978-0-547-31534-8
PTS:
LOC:
TOP:
KEY:
NOT:
38. ANS:
20
1
DIF: Level B
REF: MC100193
NCTM.PSSM.00.MTH.9-12.MEA.2.b | NCTM.PSSM.00.MTH.9-12.PRS.2
Lesson 11.4 Use Geometric Probability
word | real-life | geometric | probability | simple
MSC: DOK 2
978-0-547-31534-8
PTS: 1
DIF: Level A
REF: MLGE0392
KEY: Euler's Theorem | vertices | faces | edges
NOT: 978-0-547-31534-8
39. ANS:
a. 6
b. 10
c. 6
TOP: Lesson 11.5 Explore Solids
MSC: DOK 2
PTS: 1
DIF: Level B
KEY: faces | edges | vertices | pyramid
40. ANS:
a. 7
b. 12
c. 7
REF: MGEO0052
MSC: DOK 2
TOP: Lesson 11.5 Explore Solids
NOT: 978-0-547-31534-8
PTS: 1
DIF: Level B
KEY: pyramid | edges | vertices | faces
41. ANS:
REF: MGEO0053
MSC: DOK 2
TOP: Lesson 11.5 Explore Solids
NOT: 978-0-547-31534-8
PTS: 1
DIF: Level A
REF: PMG60622
TOP: Lesson 11.6 Volume of Prisms and Cylinders
MSC: DOK 2
NOT: 978-0-547-31534-8
42. ANS:
825
PTS: 1
DIF: Level B
REF: HLGM1167
LOC: NCTM.PSSM.00.MTH.9-12.MEA.2.b
KEY: volume | prism
LOC: NCTM.PSSM.00.MTH.9-12.MEA.2.b
TOP: Lesson 11.6 Volume of Prisms and Cylinders
MSC: DOK 2
NOT: 978-0-547-31534-8
43. ANS:
KEY: right | volume | prism
PTS:
LOC:
TOP:
MSC:
44. ANS:
Area:
NAT: NT.CCSS.MTH.10.9-12.G.GMD.3
1
DIF: Level B
REF: HLGM1168
NCTM.PSSM.00.MTH.9-12.MEA.2.b
Lesson 11.6 Volume of Prisms and Cylinders
DOK 2
NOT: 978-0-547-31534-8
KEY: volume | cylinder
, Volume:
PTS: 1
DIF: Level B
REF: HLGM1169
LOC: NCTM.PSSM.00.MTH.9-12.MEA.2.b
TOP: Lesson 11.6 Volume of Prisms and Cylinders
MSC: DOK 2
NOT: 978-0-547-31534-8
45. ANS:
80 in.3
NAT: NT.CCSS.MTH.10.9-12.G.GMD.3
KEY: surface | cylinder | area | volume
PTS:
LOC:
TOP:
MSC:
46. ANS:
1
DIF: Level C
REF: GEO.12.04.FR.10
NCTM.PSSM.00.MTH.9-12.MEA.2.b
Lesson 11.6 Volume of Prisms and Cylinders
KEY: Free Response | oblique prism | volume
DOK 2
NOT: 978-0-547-31534-8
PTS:
NAT:
LOC:
TOP:
KEY:
MSC:
47. ANS:
13 in.
1
DIF: Level B
REF: GEO.12.05.FR.12
NT.CCSS.MTH.10.9-12.G.GMD.3
NCTM.PSSM.00.MTH.9-12.GEO.1.d | NCTM.PSSM.00.MTH.9-12.MEA.2.b
Lesson 11.7 Volumes of Pyramids and Cones
Free Response | cone | volume | height | radius | trigonometry
DOK 2
NOT: 978-0-547-31534-8
PTS: 1
DIF: Level B
REF: GGEM0095
TOP: Lesson 11.8 Surface Area and Volume of Spheres
MSC: DOK 2
NOT: 978-0-547-31534-8
48. ANS:
7:5; 7:5; 343:125
PTS:
LOC:
TOP:
MSC:
49. ANS:
1800
LOC: NCTM.PSSM.00.MTH.9-12.MEA.2.b
KEY: sphere | surface area
1
DIF: Level B
REF: MLGE0437
NCTM.PSSM.00.MTH.9-12.GEO.1.b | NCTM.PSSM.00.MTH.9-12.MEA.2.b
Lesson 11.9 Explore Similar Solids
KEY: ratio | area | similar | volume | length
DOK 2
NOT: 978-0-547-31534-8
PTS: 1
DIF: Level B
REF: HLGM1201
TOP: Lesson 11.9 Explore Similar Solids
KEY: radius | area | surface | sphere
50. ANS:
MSC: DOK 2
PTS: 1
DIF: Level A
REF: PHGM1012
TOP: Lesson 11.9 Explore Similar Solids
MSC: DOK 2
NOT: 978-0-547-31534-8
NOT: 978-0-547-31534-8
LOC: NCTM.PSSM.00.MTH.9-12.GEO.1.b
KEY: ratio | area | similar | volume