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```Name: ________________________ Class: ___________________ Date: __________
ID: A
Three Dimensional Figures
1. 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.
Use formulas to find the lateral area and surface area of the given prism. Show your answer to the nearest
whole number.
2.
3. 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.
1
Name: ________________________
ID: A
Find the surface area of the cylinder in terms of  .
4.
5. 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  .
6. Find the surface area of the cylinder to the nearest whole number.
7. Allison is planning to cover the lateral surface of a large cylindrical garbage can with decorative fabric for a theme
party. The can has a diameter of 3 feet and a height of 3.5 feet. How much fabric does she need? Round to the
nearest square foot.
Find the surface area of the pyramid shown to the nearest whole number.
8.
2
Name: ________________________
ID: A
9.
10. Find the surface area of the cone in terms of  .
11. Find the lateral area of the cone to the nearest whole number.
Not drawn to scale
3
Name: ________________________
ID: A
12. Find the lateral area and surface area of the cone. Round the answers to the nearest tenth. (The figure is not drawn
to scale.)
13. Find the surface area of a conical grain storage tank that has a height of 30 meters, a diameter of 20 meters, and a
slant height of 32 meters. Round the answer to the nearest square meter.
Find the volume of the given prism. Round to the nearest tenth if necessary.
14.
Find the volume of the cylinder in terms of  .
15.
4
Name: ________________________
ID: A
16.
h = 6 and r = 3
17.
18. Find the height of the cylinder.
19. The volume of a cylinder is 980  in. 3 . The height of the cylinder is 20 in. What is the radius of the cylinder?
Find the volume of the cone shown as a decimal rounded to the nearest tenth.
20.
5
Name: ________________________
ID: A
Find the surface area of the sphere with the given dimension. Leave your answer in terms of  .
22. diameter of 16 cm
23. A balloon has a circumference of 23 cm. Use the circumference to approximate the surface area of the balloon to
the nearest square centimeter.
Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.
24.
25.
26. The volume of a sphere is 3000 m 3 . What is the surface area of the sphere to the nearest square meter?
Are the two figures similar? If so, give the similarity ratio of the smaller figure to the larger figure.
27.
6
Name: ________________________
ID: A
28.
29. The surface areas of two similar solids are 311 ft 2 and 1037 ft 2 . The volume of the larger solid is 1755 ft 3 . What is
the volume of the smaller solid?
30. The volumes of two similar solids are 729 m 3 and 125 m 3 . The surface area of the larger solid is 324 m 3 . What is
the surface area of the smaller solid?
31. A glass vase weighs 0.17 lb. How much does a similarly shaped vase of the same glass weigh if each dimension is
6 times as large?
Describe the cross section.
32.
33.
7
Name: ________________________
ID: A
34. Find the lateral area of the pyramid shown to the nearest whole number.
35. Find the lateral area of a regular pentagonal pyramid that has a slant height of 14 in. and a base side length of 6 in.
36. Find the surface area of the figure to the nearest whole number.
37. Find the slant height of the cone to the nearest whole number.
8
Name: ________________________
ID: A
Find the volume of the square pyramid shown. Round to the nearest tenth as necessary.
38.
39. What is the maximum volume of a pyramid that can fit inside a cube that has side 18 cm long?
40. A rectangular pyramid fits exactly on top of a rectangular prism. The prism has length 15 cm, width 5 cm, and
height 7 cm, and the pyramid has height 13 cm. Find the volume of the composite space figure.
9
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