7th Grade Math

Example 1 1. The surface area of a rectangular prism is 35 square inches. What is the

surface area of a similar solid that has been enlarged by a scale factor

of 7?

Example 2 2. MODELS The surface area of a ship’s hull is about 11,000 square meters.

What is the surface area, to the nearest tenth, of the hull of a model ship

that is smaller by a scale factor of _ 1001?

Example 3 3. The volume of a cylinder is about 425 cubic centimeters. What is the

volume, to the nearest tenth, of a similar solid that is smaller by a scale

factor of _^13?

Example 4 4. ART STUDIO A sink with a sliding lid in Josh’s art studio measures 16 inches

by 15 inches by 6 inches. A second sink used just for paintbrushes has a

similar shape and is smaller by a scale factor of _^1

2

. Find the surface area
and volume of the second sink.

= Step-by-Step Solutions begin on page R1.

Extra Practice begins on page EP2.

Example 1 5. The surface area of a rectangular prism is 1,300 square inches. Find the

surface area of a similar solid that is larger by a scale factor of 3.

6. The surface area of a triangular prism is 10.4 square meters. What is the
   surface area of a similar solid that is smaller by a scale factor of _^1
   4
   ?

Example 2 77 FOOD A cereal box has a surface area of 280 square inches. What is the

surface area of a similar box that is larger by a scale factor of 1.4?

8. DISPLAYS A glass display box has a surface area of 378 square inches.
   How many square inches of glass are used to create a glass display box
   with dimensions one-half the original?

Example 3 9. A cone has a volume of 9,728 cubic millimeters. What is the volume of a

similar cone one-eighth the size of the original?

10. A triangular prism has a volume of 350 cubic meters. If the dimensions
    are tripled, what is the volume of the new prism?

Example 4 11. ARCHITECTURE The model of a new

18 in.

10 in.

28 in.

apartment building is shown. The

architect plans for the building to

be 144 times the size of the model.

What will be the surface area and

volume of the new building when

it is completed?

Lesson 2C Similar Solids 657

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