Unit 9 Summary and Review
Unit 9 Summary and Review
Unit 9 Summary and Review
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Chapter 9 <strong>Summary</strong> <strong>and</strong> <strong>Review</strong><br />
9.1<br />
VOCABULARY<br />
• solid, p. 473<br />
• polyhedron, p. 473<br />
• base, p. 473<br />
• face, p. 474<br />
• edge, p. 474<br />
• prism, p. 483<br />
• surface area, p. 483<br />
VOCABULARY REVIEW<br />
Fill in the blank.<br />
1. Polyhedra are named by the shape of their __?__.<br />
2. The __?__ of a polyhedron is the sum of the areas of its faces.<br />
3. A(n) __?__ is a polyhedron with two congruent faces that lie in<br />
parallel planes.<br />
4. The __?__ of a prism are the faces of the prism that are not bases.<br />
5. The __?__ of a solid is the number of cubic units contained in its<br />
interior.<br />
SOLID FIGURES<br />
EXAMPLE<br />
Tell whether the solid is a polyhedron. If so, identify the shape of the<br />
base(s) <strong>and</strong> then name the solid.<br />
6. 7. 8.<br />
524 Chapter 9 Surface Area <strong>and</strong> Volume<br />
• lateral face, p. 484<br />
• lateral area, p. 484<br />
• cylinder, p. 485<br />
• pyramid, p. 491<br />
• height of a pyramid, p. 491<br />
• slant height of a pyramid,<br />
p. 491<br />
Tell whether the solid is a polyhedron. If so, identify<br />
the shape of the base(s) <strong>and</strong> then name the solid.<br />
The solid is formed by polygons so it is a polyhedron. There are<br />
two congruent triangular bases. This is a triangular prism.<br />
• cone, p. 493<br />
• height of a cone, p. 493<br />
• slant height of a cone, p. 493<br />
• volume, p. 500<br />
• sphere, p. 517<br />
• hemisphere, p. 517<br />
Examples on<br />
pp. 473–475
Chapter <strong>Summary</strong> <strong>and</strong> <strong>Review</strong> continued<br />
9.2<br />
9.3<br />
SURFACE AREA OF PRISMS AND CYLINDERS<br />
EXAMPLES<br />
Find the surface area to the nearest whole number.<br />
9. 10. 3 in. 11. 6 m 8 m<br />
3 ft<br />
3 ft<br />
5 ft<br />
Find the surface area to the nearest whole number.<br />
a. b.<br />
4 in.<br />
9 in.<br />
11 in.<br />
S 2B Ph S 2πr 2 2πrh<br />
2(11 p 4) (2 p 4 2 p 11)(9) 2π(4 2 ) 2π(4)(7)<br />
2(44) 270 88π<br />
358 in. 2<br />
SURFACE AREA OF PYRAMIDS AND CONES<br />
EXAMPLES<br />
6 in.<br />
7 cm<br />
≈ 276 cm 2<br />
4 cm<br />
Find the surface area to the nearest whole number.<br />
a. b.<br />
3 in.<br />
3 in.<br />
S B 1<br />
2 Pl<br />
(3 p 3) 1<br />
(4 p 3)(8)<br />
2<br />
9 1<br />
2 (12)(8)<br />
57 in. 2<br />
8 in.<br />
10 m<br />
Examples on<br />
pp. 483–486<br />
9 m<br />
Examples on<br />
pp. 491–494<br />
l 2 6 2 8 2 100 Find the slant height.<br />
l 100 = 10<br />
S πr 2 πrl Formula for surface area.<br />
π(6) 2 π(6)(10)<br />
96π<br />
8 cm<br />
≈ 302 cm 2<br />
6 cm<br />
Chapter <strong>Summary</strong> <strong>and</strong> <strong>Review</strong> 525
Chapter <strong>Summary</strong> <strong>and</strong> <strong>Review</strong> continued<br />
9.4<br />
Find the surface area of the solid. Round your answer to the nearest<br />
whole number.<br />
12. 13. 14.<br />
5 m<br />
VOLUME OF PRISMS AND CYLINDERS<br />
EXAMPLES<br />
Find the volume. Round your answer to the nearest whole number.<br />
18. 19. 20.<br />
3 in.<br />
3 m<br />
6 in.<br />
21. 22. 23. 20 in.<br />
9 ft<br />
8 in.<br />
526 Chapter 9 Surface Area <strong>and</strong> Volume<br />
4 m<br />
4 yd<br />
6 yd<br />
4 yd<br />
5 m<br />
3 cm<br />
9 cm<br />
Examples on<br />
pp. 500–502<br />
Find the volume. Round your answer to the nearest whole number.<br />
a. b.<br />
5 cm<br />
7 cm<br />
5 m<br />
15. 16. 17.<br />
6 cm<br />
6 ft<br />
4 ft<br />
V Bh V πr 2 h<br />
(7 p 9)(5) π(6 2 )(8)<br />
(63)(5) 288π<br />
315 cm 3<br />
7 m<br />
8 cm<br />
9 cm<br />
4 ft<br />
B ≈ 6.9 ft 2<br />
4 ft<br />
8 in.<br />
11 in.<br />
6 m<br />
≈ 905 m 3<br />
4 ft<br />
6 ft<br />
12 ft<br />
5 ft<br />
6 ft<br />
14 in.
Chapter <strong>Summary</strong> <strong>and</strong> <strong>Review</strong> continued<br />
9.5<br />
9.6<br />
VOLUME OF PYRAMIDS AND CONES<br />
EXAMPLES<br />
Find the volume. Round your answer to the nearest whole number.<br />
24. 25. 10 in.<br />
26.<br />
6 m<br />
12 in.<br />
3 m<br />
5 m<br />
Examples on<br />
pp. 510–512<br />
Find the volume. Round your answer to the nearest whole number.<br />
a. b.<br />
12 in.<br />
10 in.<br />
10 in.<br />
V 1<br />
Bh V 1<br />
3 3 πr 2 h<br />
1<br />
(10 p 10)(12) 400 in.3<br />
3<br />
SURFACE AREA AND VOLUME OF SPHERES<br />
EXAMPLE<br />
Surface area 4πr 2<br />
12 ft<br />
Find the surface area <strong>and</strong> the volume of the sphere. Round your<br />
answer to the nearest whole number.<br />
27. 28.<br />
18 cm<br />
29.<br />
6.5 m<br />
4 ft<br />
1<br />
3 π(42 )(12) 64π ≈ 201 ft 3<br />
Find the surface area <strong>and</strong> the volume of the sphere.<br />
Round your answer to the nearest whole number.<br />
Volume 4 3<br />
πr<br />
3<br />
4π(6 2 ) 4<br />
3 π(63 )<br />
144π 288π<br />
≈ 452 in. 2<br />
≈ 905 in. 3<br />
7.7 ft<br />
15 cm<br />
9 cm<br />
Examples on<br />
pp. 517–519<br />
6 in.<br />
Chapter <strong>Summary</strong> <strong>and</strong> <strong>Review</strong> 527
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