Study Guide:
Review
chapter
11
CHAPTER
Organizer
For a
complete list
of postulates,
theorems, and
corollaries,
see p. PT2.
Vocabulary
center of a sphere
face
radius of a sphere
Objective: Help students
cone
great circle
sphere
organize and review key concepts
and skills in this chapter.
cross section
hemisphere
vertex
cube
net
volume
cylinder
prism
edge
pyramid
Online Edition
Multilingual Glossary
Complete the sentences below with vocabulary words from the list above.
Countdown
1. A(n) ? is a flat surface of a solid.
−−−−
2. A name given to the intersection of a three-dimensional figure and a plane is
Resources
? .
−−−−
11-1 Solid Geometry
Multilingual Glossary
EXERCISES
EXAMPLES
Lesson Tutorial Videos
■
Classify the figure. Name the
vertices, edges, and bases.
pentagonal prism
A
B
G
F
vertices: A, B, C, D, E, F,
C
G, H, J, K
H
J
−− −− −− −− −− −− −−− −− −−
edges: AB, BC, CD, DE, AE, FG, GH, HJ, JK,
−− −− −− −− −− −−
KF, AF, EK, DJ, CH, BG
Answers
1. oblique prism
2. face
3. cone; vertex: M; edges: none;
base: ⊙L
E
K
■
5. cylinder
3.
N
4.
M
D
bases: ABCDE, FGHJK
4. rectangular pyramid; vertices: N,
̶̶ ̶̶ ̶̶
P, Q, R, S; edges: NP, NQ, NR,
̶̶ ̶̶ ̶̶ ̶̶ ̶̶
NS, PQ, QR, RS, SP; base: PQRS
Classify each figure. Name the vertices, edges,
and bases.
P
S
Q
R
L
Describe the three-dimensional figure that can be
made from the given net.
5.
6.
Describe the three-dimensional
figure that can be made from
the given net.
The net forms a rectangular prism.
6. square pyramid
7. V = 1080 ft 3
11-2 Volume of Prisms and Cylinders
8. V = 1651.7 cm 3
EXERCISES
EXAMPLES
■
Find the volume of each prism.
Find the volume of
the prism.
( )
1 aP h
V = Bh = _
2
1 (4 √3
�)(48)(12)
=_
2
� ≈ 1995.3 cm 3
= 1152 √3
778
Chapter 11
7.
8.
10 ft
12 ft
8 cm
9 ft
15 cm
8 cm
Chapter 11 Spatial Reasoning
CS10_G_MESE612294_C11RV.indd 778
778
12 cm
2/24/11 1:08:27 AM
■
Find the volume of the cylinder.
Answers
Find the volume of each cylinder.
9.
10.
2
V = πr 2h = π(6) (14)
9. V = 900π in 3
3m
10. V = 45π m 3
= 504π ≈ 1583.4 ft 3
5m
16 in.
6 ft
11. V = 112 m 3
14 ft
12. V ≈ 10.4 cm 3
15 in.
13. V = 120π cm 3
14. V = 48π ft 3
15. V = 512π ft 3
11-3 Volume of Pyramids and Cones
Find the volume of
the pyramid.
1 Bh = _
1 (8 · 3)(14)
V=_
3
3
= 112 in 3
Find the volume of each pyramid or cone.
11. a hexagonal pyramid with base area 42 m 2 and
height 8 m
14 in.
3 in.
8 in.
■
_
EXERCISES
EXAMPLES
■
16. V ≈ 1533.3 cm 3
500π 3
m
17. V =
3
18. S = 144π in 2
19. d = 16 ft
20. S ≈ 338.3 cm 2; V ≈ 293.5 cm 3
21. S ≈ 245.0 ft 2; ≈ 84.8 ft 3
12. an equilateral triangular pyramid with base edge
3 cm and height 8 cm
13. a cone with diameter 12 cm and height 10 cm
Find the volume of the cone.
14. a cone with base area 16π ft 2 and height 9 ft
1 πr 2h = _
1 π(9)2(16)
V=_
3
3
= 432π ft 3 ≈ 1357.2 ft 3
Find the volume of each composite figure.
8 ft
15.
16.
16 ft
16 cm
9 ft
12 ft
10 cm
10 cm
10 cm
11-4 Spheres
EXERCISES
EXAMPLE
■
Find the volume and surface
area of the sphere. Give your
answers in terms of π.
4 π(9)3 = 972π m 2
4 πr 3 = _
V=_
3
3
S = 4πr 2 = 4π(9)2 = 324π m 2
M CS10_G_MESE612294_C11RV.indd 779
18 m
Find each measurement. Give your answers in terms
of π.
17. the volume of a sphere with surface area 100π m 2
18. the surface area of a sphere with volume 288π in 3
19. the diameter of a sphere with surface area
256π ft 2
Find the surface area and volume of each composite
figure.
6 cm
20.
21.
7 ft
3 ft
5 cm
7 cm
10 cm
Study Guide: Review
779
2/24/11 1:08:36 AM
Study Guide: Review
779