CHAPTER
Chapter Review
10 10-1 Solid Geometry Classify each figure. Name the vertices, edges and bases. 1.
L
2.
3.
R
T M
G
H S
U
Triangular pyramid: vertices: R, S, T, U edges: RS, SU, RU, RT, TU, ST bases: triangle STU.
Cylinder : vertices: none, edges: none, bases: L and M
Cone: vertices G, edges: none, bases: H
Describe the three-dimensional figure that can be made fr om the given net. 4.
5.
The net has two congruent triangular faces. The remaining faces are rectangles, so the net forms a triangular prism.
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6.
The net has one circle and a circle with a pie piece missing. This net forms a cone.
225
The net has six congruent rectangles. The remaining faces are 2 hexagons, so the net forms a hexagonal prism.
Geometry
CHAPTER 10 REVIEW CONTINUED
Describe the cross section. 7.
8.
Circle
9.
Triangle
Hexagon
10-2 Representations of Three-Dimensional Figures Use the figure made of unit cube f or Problems 10 and 11. Assume there are no hid den cubes. 10. Draw all six orthographic views.
top
right side
left side
bottom
front
back
11. Draw an isometric view.
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Geometry
CHAPTER 10 REVIEW CONTINUED
12. Draw the block letter F in one-point perspective.
13. Draw the block letter F in two-point perspective.
10-3 Formulas in Three Dimensions Find the number of vertices, edges, and faces of each polyhedron. Use your results to verify the Euler’s formula. 14. rectangular prism vertices: 8, edges: 12, faces: 6 VEF2 8 12 6 2
15. pentagonal pyramid vertices: 6, edges: 10, faces: 6 VEF2 6 10 6 2
16. rectangular pyramid vertices: 5, edges: 8, faces: 5 VEF2 5852
17. A fish tank is in the shape of a rectangular prism. The base of the fish tank is 2 ft by 3 ft and has a 4.5 ft diagonal. What is the height of the fish tank? 2.7 ft
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227
Geometry
CHAPTER 10 REVIEW CONTINUED
Find the distance between the given points. Find the midpoint of the segments with the given end points. Round to the nearest tenth, if necessary. 18. (0, 0, 0) and (6, 8, 12)
19. (4, 1, –1) and (3, –3, 5)
20. (5, 6, –2) and (4, –2, 6)
distance 7.3 units; midpoint M (3.5, 1, 2)
distance 15.6 units; midpoint M (3, 4, 6)
distance 11.4 units; midpoint M (4.5, 2, 2)
10-4 Surface Area of Prisms and Cylinders Find the surface area of eac h figure. Round to the nearest tenth, if necessary. 21. 5 in.
22.
23. 2 in.
24 in.
5 in.
6 ft 4 ft
4 in.
30 in.
SA 1980 in.2
6 in.
SA 251.3 ft2
185.7 in.2
24. The dimensions of a 12 in. by 9 in. by 24 in. right rectangular prism are 2 multiplied by 3. Describe the affect on the surface area. Answers may vary: The surface area will be 4 of the original surface area. 9
10-5 Surface Area of Pyramids and Cones Find the surface area of eac h figure. Round to the nearest tenth, if necessary. 25. a regular square pyramid with base edge length of 6 ft and slant height 14 ft 204 ft2
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26. a right cone with diameter 32 cm and height 18 cm 2014.8 cm2
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Geometry
CHAPTER 10 REVIEW CONTINUED
27. the composite figure formed by a cone and a cylinder 10 cm
S (cone lateral area) (cylinder lateral area) (base area) S 16.25 20 6.25 S 42.5 cm2
5 cm 4 cm
10-6 Volume of Prisms and Cylinders Find the volume of each figure. Round to the nearest tenth if necessar y. 28. a regular hexagonal prism with base area 192 in.2 and height 24 in.
29. a cylinder with radius 3 yd and height 11 yd
4608 in3
311.2 yd.3
30. A brick patio measures 8 ft by 10 ft by 3 in. Find the volume of the bricks. If the density of a brick is about 140 pounds per cubic foot, what is the weight of the patio in pounds? 20 ft3; 2800 pounds3 31. The dimensions of a cylinder with diameter 2 ft and height 1 ft are reduced by half. Describe the affect on the volume. The volume will be 1 the original volume. 8
10-7 Volume of Pyramids and Cones Find the volume of each figure. Round to the nearest tenth, if necessary. 32.
18 m
14 m
33.
34. 18 m 25 in.
9 in.
V 923.6 m3
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9 in.
V 664 in.3 229
6m 8m
8m
V 758.4 m3
Geometry
CHAPTER 10 REVIEW CONTINUED
10-8 Spheres Find the surface area and the v olume of each figure. 35. a sphere with diameter 6 in. SA 113 in.2, V 113.1 in.3
36. a hemisphere with radius 5 cm SA 235.6 cm2, V 262 cm3
37. A playground ball has a diameter of about 9 in. A bouncy ball has the diameter of 3 in. About how many more times as great is the volume of the playground ball as the volume of a bouncy ball? The volume of the playground ball is about 27 times lar ger than that of the bouncy ball.
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Geometry
