Chapter 11 Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Use Euler’s Formula to find the missing number.
Vertices: 16
Edges: 37
Faces:
a. 24
____
b. 22
c. 23
d. 26
2. Mario’s company makes unusually shaped imitation gemstones. One gemstone had 10 faces and 12 vertices.
How many edges did the gemstone have?
a. 20 edges
b. 23 edges
c. 25 edges
d. 22 edges
Describe the cross section.
____
____
____
3.
a. cube
b. trapezoid
c. pentagon
d. square
a. pentagon
b. trapezoid
c. hexagon
d. cube
4.
5. Pierre built the model shown in the diagram below for a social studies project. He wants to be able to show
the inside of his model, so he sliced the figure as shown. Describe the cross section he created.
a. hexagon
b. pentagon
c. pyramid
d. rectangle
Use formulas to find the lateral area and surface area of the given prism. Show your answer to the
nearest whole number.
____
6.
5.83
23
3
5
Not drawn to scale
a. 318.09 m ; 326 m
b. 295 m ; 333 m
____
c. 295 m ; 348 m
d. 318.09 m ; 333 m
7.
8m
5m
14 m
Not drawn to scale
a. 220 m ; 332 m
b. 220 m ; 444 m
____
c. 364 m ; 444 m
d. 364 m ; 332 m
8. A jewelry store buys small boxes in which to wrap items that they sell. The diagram below shows one of the
boxes. Find the lateral area and the surface area of the box to the nearest whole number.
8 cm
1.22 cm
11 cm
Not drawn to scale
a. 46 cm ; 222 cm
b. 46 cm ; 310 cm
c. 23 cm ; 310 cm
d. 23 cm ; 222 cm
Find the surface area of the cylinder in terms of
____
.
9.
8 in.
11 in.
Not drawn to scale
a. 688 in.
b. 304
in.
c. 176
in.
d. 208
in.
cm
c. 812
cm
d. 308
cm
____ 10.
14 cm
15 cm
Not drawn to scale
a. 518 cm
b. 602
____ 11. The radius of the base of a cylinder is 28 cm and its height is 48 cm. Find the surface area of the cylinder in
terms of .
a. 4332 cm
b. 4256 cm
c. 4208 cm
d. 4228 cm
____ 12. Find the surface area of the cylinder to the nearest whole number.
20 in.
10 in.
Not drawn to scale
a. 1257 in.
b. 4200 in.
c. 3770 in.
d. 14002 in.
Find the surface area of the pyramid shown to the nearest whole number.
____ 13.
6 ft
5 ft
5 ft
Not drawn to scale
a. 85 ft
b. 145 ft
c. 60 ft
d. 25 ft
c. 819 m
d. 240 m
____ 14.
10 m
8m
5 2
Not drawn to scale
a. 410 m
b. 393 m
____ 15. Find the lateral area of the pyramid shown to the nearest whole number.
25 yd
43 yd
Not drawn to scale
a. 4278 yd
b. 2836 yd
c. 5671 yd
d. 2150 yd
____ 16. Find the surface area of the figure to the nearest whole number.
a. 310 ft
b. 155 ft
____ 17. Find the surface area of the cone in terms of
c. 135 ft
d. 74 ft
c. 51
d. 49.5 cm
.
15 cm
3 cm
Not drawn to scale
a. 54
cm
b. 99
cm
cm
____ 18. Find the lateral area of the cone to the nearest whole number.
Not drawn to scale
a. 7540 m
b. 3770 m
c. 4712 m
d. 9425 m
____ 19. Find the lateral area and surface area of the cone. Round the answers to the nearest tenth. (The figure is not
drawn to scale.)
a. L.A. = 395.8 ft ; S.A. = 791.7 ft
b. L.A. = 1583.4 ft ; S.A. = 1244.1 ft
c. L.A. = 622.0 ft ; S.A. = 791.7 ft
d. L.A. = 791.7 ft ; S.A. = 1244.1 ft
Find the volume of the given prism. Round to the nearest tenth if necessary.
____ 20.
4 ft
7 ft
11 ft
Not drawn to scale
a. 308 ft
b. 301 ft
c. 298 ft
d. 312 ft
____ 21.
22 yd
15 yd
15 yd
15 yd
Not drawn to scale
a. 2143.4 yd
b. 1750.1 yd
c. 4286.8 yd
d. 2475.0 yd
a. 17 m
b. 34 m
c. 8.5 m
d. 1 m
____ 22.
____ 23. Find the volume of the composite space figure to the nearest whole number.
a. 170 cm
b. 180 cm
Find the volume of the cylinder in terms of
c. 120 cm
d. 60 cm
.
____ 24.
7 in.
10 in.
Not drawn to scale
a. 140
in.
b. 490
in.
c. 70
in.
d. 245
in.
____ 25.
12 m
2.5 m
Not drawn to scale
a. 75
b. 60 m
m
c. 37.5
m
d. 187.5
m
____ 26.
h = 6 and r = 3
a. 27 in.
b. 108
in.
c. 54
in.
d. 324
in.
____ 27. Find the height of the cylinder.
a. 2.4 in.
b. 7.2 in.
c. 14.4
d. 4.8 in.
Find the volume of the square pyramid shown. Round to the nearest tenth as necessary.
____ 28.
10 cm
12 cm
12 cm
Not drawn to scale
a. 40 cm
b. 480 cm
c. 147.3 cm
d. 720 cm
c. 4608 ft
d. 3072 ft
____ 29.
20 ft
24 ft
Not drawn to scale
a. 192 ft
b. 9216 ft
Find the volume of the cone shown as a decimal rounded to the nearest tenth.
____ 30.
14 yd
5 yd
Not drawn to scale
a. 366.5 yd
b. 1026.3 yd
c. 73.3 yd
d. 549.8 yd
c. 5598.3 in.
d. 2799.2 in.
____ 31.
22 in.
18 in.
Not drawn to scale
a. 207.3 in.
b. 1866.1 in.
____ 32.
22 m
12 m
Not drawn to scale
a. 552.9 m
b. 829.4 m
c. 1,244.1 m
d. 3,317.5 m
Find the surface area of the sphere with the given dimension. Leave your answer in terms of
____ 33. diameter of 16 cm
a. 256 cm
b. 128
cm
c. 32
____ 34. radius of 30 m
a. 1,800 m
b. 900
m
c. 3,600
d. 1024
cm
m
d. 450
.
cm
m
Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.
____ 35.
5 mm
a. 262 mm
b. 524 mm
c. 314 mm
d. 105 mm
b. 442 cm
c. 236 cm
d. 14,137 cm
____ 36.
15 cm
a. 1,767 cm
Are the two figures similar? If so, give the similarity ratio of the smaller figure to the larger figure.
____ 37.
5
15
6
18
17
51
Not drawn to scale
a. yes; 1: 3
b. yes; 1: 2
____ 38.
c. yes; 1: 5
d. no
c. yes; 1 : 6
d. no
30
6
9
54
17
85
Not drawn to scale
a. yes; 1 : 10
b. yes; 1 : 5
____ 39. Find the similarity ratio of a cube with volume 729 m to a cube with volume 3375 m .
a. 81 : 225
b. 3 : 5
c. 5 : 3
d. 225 : 81
____ 40. Find the similarity ratio of a prism with surface area 36 ft to a similar prism with surface area 225 ft .
a. 2 : 5
b. 3375 : 216
c. 5 : 2
d. 216 : 3375
____ 41. The surface areas of two similar solids are 311 ft and 1037 ft . The volume of the larger solid is 1755 ft .
What is the volume of the smaller solid?
a. 288 ft
b. 1,755 ft
c. 961 ft
d. 789 ft
____ 42. The volumes of two similar solids are 729 m and 125 m . The surface area of the larger solid is 324 m .
What is the surface area of the smaller solid?
a. 56 m
b. 100 m
c. 500 m
d. 200 m
Other
43. Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and
sides of the cylinder. The diameter of each ball is 13 cm.
a.
b.
c.
What is the volume of the cylinder? Explain your method for finding the volume.
What is the total volume of the three balls? Explain your method for finding the total
volume.
What percent of the volume of the container is occupied by the three balls? Explain
how you find the percent.
Chapter 11 Practice Test
Answer Section
MULTIPLE CHOICE
1. ANS:
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2. ANS:
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9. ANS:
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10. ANS:
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11. ANS:
REF:
C
PTS: 1
DIF: L2
11-1 Space Figures and Cross Sections
11-1.1 Identifying Nets of Space Figures
TOP: 11-1 Example 2
polyhedron | face | vertices | edge | Euler's Formula
A
PTS: 1
DIF: L3
11-1 Space Figures and Cross Sections
11-1.1 Identifying Nets of Space Figures
TOP: 11-1 Example 2
edge | Euler's Formula | face | polyhedron | problem solving | word problem | vertices
D
PTS: 1
DIF: L2
11-1 Space Figures and Cross Sections
OBJ: 11-1.2 Describing Cross Sections
11-1 Example 4
KEY: cross section
A
PTS: 1
DIF: L2
11-1 Space Figures and Cross Sections
OBJ: 11-1.2 Describing Cross Sections
11-1 Example 4
KEY: cross section
B
PTS: 1
DIF: L3
11-1 Space Figures and Cross Sections
OBJ: 11-1.2 Describing Cross Sections
11-1 Example 4
KEY: cross section | word problem
D
PTS: 1
DIF: L2
11-2 Surface Areas of Prisms and Cylinders
11-2.1 Finding Surface Area of a Prism
STA: CA GEOM 8.0| CA GEOM 9.0
11-2 Example 2
surface area formulas | lateral area | surface area | prism | surface area of a prism
B
PTS: 1
DIF: L2
11-2 Surface Areas of Prisms and Cylinders
11-2.1 Finding Surface Area of a Prism
STA: CA GEOM 8.0| CA GEOM 9.0
11-2 Example 2
surface area formulas | lateral area | surface area | prism | surface area of a prism
A
PTS: 1
DIF: L3
11-2 Surface Areas of Prisms and Cylinders
11-2.1 Finding Surface Area of a Prism
STA: CA GEOM 8.0| CA GEOM 9.0
11-2 Example 2
surface area of a prism | lateral area | prism | surface area formulas | surface area | word problem
B
PTS: 1
DIF: L2
11-2 Surface Areas of Prisms and Cylinders
11-2.2 Finding Surface Area of a Cylinder
STA: CA GEOM 8.0| CA GEOM 9.0
11-2 Example 3
surface area of a cylinder | cylinder | surface area formulas | surface area
D
PTS: 1
DIF: L2
11-2 Surface Areas of Prisms and Cylinders
11-2.2 Finding Surface Area of a Cylinder
STA: CA GEOM 8.0| CA GEOM 9.0
11-2 Example 3
surface area of a cylinder | cylinder | surface area formulas | surface area
B
PTS: 1
DIF: L2
11-2 Surface Areas of Prisms and Cylinders
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
OBJ: 11-2.2 Finding Surface Area of a Cylinder
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-2 Example 3
KEY: cylinder | surface area of a cylinder | surface area formulas | surface area | word problem
ANS: C
PTS: 1
DIF: L3
REF: 11-2 Surface Areas of Prisms and Cylinders
OBJ: 11-2.2 Finding Surface Area of a Cylinder
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-2 Example 3
KEY: surface area of a cylinder | cylinder | surface area formulas | surface area
ANS: A
PTS: 1
DIF: L2
REF: 11-3 Surface Areas of Pyramids and Cones
OBJ: 11-3.1 Finding Surface Area of a Pyramid
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-3 Example 1
KEY: surface area of a pyramid | surface area | surface area formulas | pyramid
ANS: A
PTS: 1
DIF: L2
REF: 11-3 Surface Areas of Pyramids and Cones
OBJ: 11-3.1 Finding Surface Area of a Pyramid
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-3 Example 1
KEY: surface area of a pyramid | surface area formulas | pyramid
ANS: B
PTS: 1
DIF: L2
REF: 11-3 Surface Areas of Pyramids and Cones
OBJ: 11-3.1 Finding Surface Area of a Pyramid
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-3 Example 2
KEY: slant height of a pyramid | lateral area | pyramid | surface area formulas | Pythagorean Theorem
ANS: B
PTS: 1
DIF: L3
REF: 11-3 Surface Areas of Pyramids and Cones
OBJ: 11-3.1 Finding Surface Area of a Pyramid
STA: CA GEOM 8.0| CA GEOM 9.0
KEY: surface area of a prism | surface area of a pyramid | lateral area | prism | problem solving | pyramid |
surface area formulas | surface area
ANS: A
PTS: 1
DIF: L2
REF: 11-3 Surface Areas of Pyramids and Cones
OBJ: 11-3.2 Finding Surface Area of a Cone
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-3 Example 3
KEY: surface area of a cone | surface area formulas | surface area | cone
ANS: C
PTS: 1
DIF: L3
REF: 11-3 Surface Areas of Pyramids and Cones
OBJ: 11-3.2 Finding Surface Area of a Cone
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-3 Example 4
KEY: cone | surface area of a cone | surface area formulas | surface area
ANS: D
PTS: 1
DIF: L3
REF: 11-3 Surface Areas of Pyramids and Cones
OBJ: 11-3.2 Finding Surface Area of a Cone
STA: CA GEOM 8.0| CA GEOM 9.0
KEY: cone | surface area of a cone | lateral area | surface area formulas | surface area
ANS: A
PTS: 1
DIF: L2
REF: 11-4 Volumes of Prisms and Cylinders
OBJ: 11-4.1 Finding Volume of a Prism
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-4 Example 1
KEY: volume of a rectangular prism | volume formulas | volume | prism
ANS: A
PTS: 1
DIF: L2
REF: 11-4 Volumes of Prisms and Cylinders
OBJ: 11-4.1 Finding Volume of a Prism
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-4 Example 2
KEY: volume of a triangular prism | volume formulas | volume | prism
22. ANS: A
PTS: 1
DIF: L3
REF: 11-4 Volumes of Prisms and Cylinders
OBJ: 11-4.1 Finding Volume of a Prism
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-4 Example 2
KEY: volume of a triangular prism | volume formulas | volume | prism
23. ANS: B
PTS: 1
DIF: L3
REF: 11-4 Volumes of Prisms and Cylinders
OBJ: 11-4.1 Finding Volume of a Prism
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-4 Example 1
KEY: volume of a rectangular prism | problem solving | volume formulas | volume
24. ANS: B
PTS: 1
DIF: L2
REF: 11-4 Volumes of Prisms and Cylinders
OBJ: 11-4.2 Finding Volume of a Cylinder
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-4 Example 3
KEY: volume of a cylinder | cylinder | volume formulas | volume
25. ANS: A
PTS: 1
DIF: L2
REF: 11-4 Volumes of Prisms and Cylinders
OBJ: 11-4.2 Finding Volume of a Cylinder
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-4 Example 3
KEY: volume of a cylinder | cylinder | volume formulas | volume
26. ANS: C
PTS: 1
DIF: L2
REF: 11-4 Volumes of Prisms and Cylinders
OBJ: 11-4.2 Finding Volume of a Cylinder
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-4 Example 3
KEY: volume of a cylinder | cylinder | volume formulas | volume | oblique cylinder
27. ANS: A
PTS: 1
DIF: L3
REF: 11-4 Volumes of Prisms and Cylinders
OBJ: 11-4.2 Finding Volume of a Cylinder
STA: CA GEOM 8.0| CA GEOM 9.0
KEY: cylinder | volume of a cylinder | volume
28. ANS: B
PTS: 1
DIF: L2
REF: 11-5 Volumes of Pyramids and Cones
OBJ: 11-5.1 Finding Volume of a Pyramid
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-5 Example 1
KEY: volume of a pyramid | pyramid | volume formulas | volume
29. ANS: D
PTS: 1
DIF: L2
REF: 11-5 Volumes of Pyramids and Cones
OBJ: 11-5.1 Finding Volume of a Pyramid
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-5 Example 1
KEY: volume of a pyramid | pyramid | volume formulas | volume | height of a pyramid | Pythagorean
Theorem
30. ANS: A
PTS: 1
DIF: L2
REF: 11-5 Volumes of Pyramids and Cones
OBJ: 11-5.2 Finding Volume of a Cone
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-5 Example 3
KEY: volume of a cone | cone | volume formulas | volume
31. ANS: B
PTS: 1
DIF: L2
REF: 11-5 Volumes of Pyramids and Cones
OBJ: 11-5.2 Finding Volume of a Cone
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-5 Example 3
KEY: volume of a cone | oblique cone | volume formulas | volume
32. ANS: B
PTS: 1
DIF: L2
REF: 11-5 Volumes of Pyramids and Cones
OBJ: 11-5.2 Finding Volume of a Cone
STA: CA GEOM 8.0| CA GEOM 9.0
TOP: 11-5 Example 4
KEY: volume of a cone | volume formulas | volume | cone
33. ANS: A
PTS: 1
DIF: L2
REF: 11-6 Surface Areas and Volumes of Spheres
34.
35.
36.
37.
38.
39.
40.
41.
42.
OBJ:
TOP:
KEY:
ANS:
REF:
OBJ:
TOP:
KEY:
ANS:
REF:
OBJ:
TOP:
ANS:
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OBJ:
TOP:
ANS:
REF:
OBJ:
TOP:
ANS:
REF:
OBJ:
TOP:
ANS:
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OBJ:
TOP:
ANS:
REF:
OBJ:
TOP:
ANS:
REF:
OBJ:
TOP:
KEY:
ANS:
REF:
OBJ:
TOP:
KEY:
11-6.1 Finding Surface Area and Volume of a Sphere
STA: CA GEOM 8.0| CA GEOM 9.0
11-6 Example 1
surface area of a sphere | surface area formulas | surface area | sphere
C
PTS: 1
DIF: L2
11-6 Surface Areas and Volumes of Spheres
11-6.1 Finding Surface Area and Volume of a Sphere
STA: CA GEOM 8.0| CA GEOM 9.0
11-6 Example 1
surface area of a sphere | surface area formulas | surface area | sphere
B
PTS: 1
DIF: L2
11-6 Surface Areas and Volumes of Spheres
11-6.1 Finding Surface Area and Volume of a Sphere
STA: CA GEOM 8.0| CA GEOM 9.0
11-6 Example 3
KEY: volume of a sphere | sphere | volume formulas | volume
A
PTS: 1
DIF: L2
11-6 Surface Areas and Volumes of Spheres
11-6.1 Finding Surface Area and Volume of a Sphere
STA: CA GEOM 8.0| CA GEOM 9.0
11-6 Example 3
KEY: volume of a sphere | sphere | volume formulas | volume
A
PTS: 1
DIF: L2
11-7 Areas and Volumes of Similar Solids
11-7.1 Finding Relationships in Area and Volume
STA: CA GEOM 11.0
11-7 Example 1
KEY: similar solids | similarity ratio | rectangular prism
D
PTS: 1
DIF: L2
11-7 Areas and Volumes of Similar Solids
11-7.1 Finding Relationships in Area and Volume
STA: CA GEOM 11.0
11-7 Example 1
KEY: similar solids | similarity ratio | rectangular prism
B
PTS: 1
DIF: L2
11-7 Areas and Volumes of Similar Solids
11-7.1 Finding Relationships in Area and Volume
STA: CA GEOM 11.0
11-7 Example 2
KEY: similarity ratio | volumes of similar solids
A
PTS: 1
DIF: L2
11-7 Areas and Volumes of Similar Solids
11-7.1 Finding Relationships in Area and Volume
STA: CA GEOM 11.0
11-7 Example 2
KEY: similarity ratio | surface areas of similar solids | prism
A
PTS: 1
DIF: L2
11-7 Areas and Volumes of Similar Solids
11-7.1 Finding Relationships in Area and Volume
STA: CA GEOM 11.0
11-7 Example 3
similarity ratio | ratio of surface areas of similar solids | ratio of volumes of similar solids
B
PTS: 1
DIF: L2
11-7 Areas and Volumes of Similar Solids
11-7.1 Finding Relationships in Area and Volume
STA: CA GEOM 11.0
11-7 Example 3
similarity ratio | surface areas of similar solids | volumes of similar solids
OTHER
43. ANS:
To find the volume of the cylinder, use the formula. You need to use the height and the
a.
radius of the cylinder. The radius is the radius of the ball or
. The
height of the cylinder is
since 3 balls occupy the cylinder.
b.
c.
V =
Use the formula for the volume of a cylinder.
V =
Substitute 6.5 for r and 39 for h.
V
5177
Use a calculator.
The volume of the cylinder is about 5177 cm .
Use the formula for volume of a sphere to find the volume of one sphere. Then
multiply the result by 3.
V
=
Use the formula for the volume of a sphere.
V
=
Substitute 6.5 for r.
V
1150
Use a calculator.
The volume of the three balls is about
cm , or 3450 cm .
To find the percent of the cylinder’s volume occupied by the balls, write a fraction with
the volume of the balls as the numerator and the volume of the cylinder as the
denominator. Then write the fraction as a percent.
PTS: 1
DIF: L4
REF: 11-6 Surface Areas and Volumes of Spheres
OBJ: 11-6.1 Finding Surface Area and Volume of a Sphere
STA: CA GEOM 8.0| CA GEOM 9.0
KEY: cylinder | volume of a cylinder | volume of a sphere | multi-part question | problem solving | sphere |
volume formulas | volume | writing in math