Chapter 11 - Find the total area and volume of the following prisms.
1)
2)
3)
4)
Find the area of the base, total area, and volume of the following :
1. A rectangular prism with length 7 cm, width 6 cm, and height 2 cm.
2. A rectangular solid with length 3 m, width 1.2 m, and height .5 m.
3. Find the total area and volume of a cube with edge 5 cm.
4. Find the total area of a right hexagonal prism with height 12 and base edges 3, 4, 5, 6, 5.2, and 6.3.
5. The total area of a cube is 216 cm2. Find the length of an edge. __________
6. The base of a right prism is a square with edge 4 cm. The volume is 64 cm3. Find the height. ___________
Sketch the prism with base and height as described and find the total area and volume:
7. Triangle with sides 6,8,10; h = 12
8. Equilateral ∆ with side 6; h = 8
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Cylinders For each cylinder or prism, find the area of the base, surface area and volume
1.
2.
20
ft
3.
4.
11 ft
5. Find the total area of the toilet paper.
6.
7. Find the volume of the composite space figure.
Find the volume of the space between the
cube and the cylinder.
8. The surface area of a cylindrical septic tank is
290π ft2 and the radius is 5 ft. Find the height.
Find the following for a right cylinder.
9. r = 6, h = 8 B = ______
10. r = 7, h = 24
T.A. = _______ V= __________
B = ______
T.A. = _______ V= _______
14. The lateral area of a cylinder is 100π. If r = 5, find h.
15. The total area of a cylinder is 144π. If r = h, find r.
16. Cylinder A has radius 4 and height 6. Cylinder B has radius 6 and height 4.
_______a) which one has the greater lateral area?
_______a) which one has the greater volume?
2
Spheres
Radius
1.
7
2.
5
3.
½
4.
3
4
5.
6.
2
k
Area
7.
64
324
Volume
9. Find the surface area and volume of a sphere with a radius of 5in. Leave your answer in terms of π.
10. The world’s largest disco ball has a diameter of 5.01m. Find the surface area and volume of the disco ball.
11. The circumference of a rubber ball is 13cm. Find the surface area to the nearest whole number.
Pyramids and Cones
Base Lateral faces Slant height –
Height/Altitude –
3
Find the total surface area and volume of the composite space figures.
4
7.1 Similar Figures
If 2 figures are similar then:
(1) CORRESPONDING ANGLES ARE ______________
(2) CORRESPONDING SIDES ARE ________________
THE REDUCED RATIO OF 2 CORR. SIDES IS CALLED THE ____________ _________.
IF 2 FIGURES ARE SIMILAR, THEN THE RATIO OF THEIR ____________IS = TO THE _____________ ______________.
SIMILARITY STATEMENT: Ex. ∆ BIG ~ ∆ MAN
1.) B  ______
I  ___
BI  IG 
2)
MN
G
Ex. 3
12
I
∆GWT ~ ∆ GIH
8
14
y
W
E
G  ____
Scale Factor:
H
10
x
T
Determine whether the polygons are similar. If so, write the similarity ratio
and a similarity statement. If not, explain why not.
1.
3. parallelograms EFGH and TUVW
2.
4. CDE and LMN
Tell whether the polygons must be similar based on the information given in the figures.
5.
.
5
7.
8.
7.3 Identifying Similar Triangles
Angle-Angle Similarity Postulate (AA~) If two angles are congruent to two angles of another triangle, then the
triangles are similar.
Side-Side-Side Similarity Theorem (SSS~)If the measures of the corresponding sides of two triangles are
proportional, then the triangles are similar.
Side-Angle-Side Similarity Theorem (SAS~) If the measures of two pair of corresponding sides of two triangles
are proportional and the included angle is congruent, then the triangles are similar.
Determine whether each pair of triangles is similar. If so, state whether it
is similar by AA~, SSS~ or SAS~.
1)
2)
_______________________________
_______________________________
3)
4)
5)
6)
6
Find x and y in each shape.
7)
8)
PRACTICE PROBLEMS
SSS~)
Write a similarity statement . Explain why the triangles are similar (AA~, SAS~,
1.
2.
CAT ~
SNA ~_____________
DOR ~___
Reason:
Reason:
Reason:
Solve for the missing sides.
4.
5.
6.
x = __________
y = __________
z = __________
3.
a = __________
b = __________
c = __________
_______
x = __________
y = __________
z = __________
7.4 Triangle Proportions
Theorem: If a line is parallel to one side of a ∆ and intersects the other two sides, then it
________________________________.
Ex. Given: BE//CD
A
Conclusion: ______________
And  C  __________; AEB  ___________
B
E
D
C
A
Ex. Given: BE//CD
Ex 1. If AB = 1, BC = 3, and AE = 2.5, find ED.
Ex. 2 If AB = 6, BC = 10, and AD = 14, find AE.
B
C
7
E
D
Theorem: On any 2 transversals, parallel lines
_______________________________________________________.
Given: Lines l // m // k
l
Conclusion: __________
m
k
Ex. 1: If a = 5 , b = 7, and d = 9, find c.
a
c
b
d
Ex. 2: If a = 2, b = 3, and c + d = 20, find d.
∆ Angle Bisector Theorem:
If a ray bisects an  of a ∆, then it divides the opposite side into segments
A
D
proportional to __________________________________________.
Given: BD bisects ABC in ∆ABC. Conclusion: __________________
Use diagram above:
Ex. 1 If BA = 12, BC = 24, and AD = 10, find AC.
Ex. 2: If BA = x, BC = 8, DA = 2 and DC = 7, find x.
C
B
Ex. 3 Find the value of x in the diagram to the right:
12
21
Find each length.
x
22
1. BH ____________________
2. MV _____________________
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