Main Idea and New Vocabulary

Key Concept: Surface Area of Similar Solids

Example 1: Surface Area of Similar Solids

Example 2: Surface Area of Similar Solids

Key Concept: Volume of Similar Solids

Example 3: Volume of Similar Solids

Example 4: Real-World Example

• Solve problems involving similar solids.

• similar solids

Surface Area of Similar Solids

The surface area of a rectangular prism is 90 square inches. What is the surface area of a similar prism that is larger by a scale factor of 5?

S.A. = 90 × 52 Multiply by the square of the scale factor.

S.A. = 90 × 25 Square 5.

S.A. = 2,250 in2 Simplify.

Answer: The surface area is 2,250 in2.

A. 36 ft2

B. 68 ft2

C. 136 ft2

D. 1,156 ft2

The surface area of a rectangular prism is 34 square feet. What is the surface area of a similar prism that is 2 times as large?

STATUE The surface area of a pyramid-shaped

statue is 160 square meters. If a scale model is

of the statue’s actual size, what is the surface

area of the model in square centimeters?

Surface Area of Similar Solids

Multiply by the square of the scale factor.

Square

Surface Area of Similar Solids

Simplify.

Answer: The surface area of the model is 4,000 cm2.

Simplify.= 4,000 cm2

Convert square meters to square centimeters.

DISPLAYS An ice cream shop has a 4-foot tall icecream cone that is displayed inside the store. Thecone has a surface area of 2,318 square inches. A

regular ice cream cone is the size of the display.

What is the surface area of the regular ice creamcone? Round to the nearest tenth if necessary.

__18

A. 30.0 in2

B. 36.2 in2

C. 144.9 in2

D. 289.8 in2

Volume of Similar Solids

A triangular prism has a volume of 96 cubic feet. If the prism is reduced to one half its original dimensions, what is the volume of the new prism?

Multiply by the cube of the scale factor.

V = 12 ft3 Simplify.

Answer: The volume of the new prism is 12 cubic feet.

Cube .

A. 486 ft3

B. 54 ft3

C. 18 ft3

D. 6 ft3

A triangular prism has a volume of 162 cubic feet. If the prism is reduced to one third its original dimensions, what is the volume of the new prism?

SOUP A jumbo-size can of tomato soup is about 3 times the size of a standard-sized can of soup. The standard can has the dimensions shown. Find the surface area and volume of the jumbo-size can.

Find the volume and surface area of the standard soup can first.

V = r 2h

≈ (3.14)(3.25)2(10)

≈ 331.67 cm3

S.A. = 2(r 2) + 2rh

≈ 2(3.14)(3.25)2 + 2(3.14)(3.25)(10)

≈ 66.33 + 204.1

≈ 270.43 cm2

Find the volume and surface area of the jumbo-size soup can using the scale factor.

V = V(3)3

≈ (331.67)(3)3

≈ 8,955 cm3

S.A. = S.A.(3)2

≈ (270.43)(3)2

≈ 2,434 cm2

Answer: The jumbo-size soup can has a volume of about 8,955 cubic centimeters and a surface area of about 2,434 square centimeters.

A. S.A. = 2,592 in2; V = 5,184 in3

B. S.A. = 3,456 in2; V = 6,912 in3

C. S.A. = 7,776 in2; V = 15,552 in3

D. S.A. = 7,776 in2; V = 46,656 in3

PACKAGING A moving company has boxes of various sizes for packing. The smallest box available has the dimensions shown below. Find the surface area and volume of a larger box that is 3 times as large.

12 in.

12 in.

12 in.