Warm Up

• A shape has 5 faces, and 5 vertices how many edges does the shape have?

• A sphere has a radius of 7.5, what is its surface area and volume?

• What is the surface area and volume of the shape?

Exploring Similar Solids

12.7

What is similar

EXAMPLE 1 Identify similar solids

Tell whether the given right rectangular prism is similar to the right rectangular prism shown at the right.

a.b.

EXAMPLE 1 Identify similar solids

SOLUTION

The prisms are similar because the ratios of corresponding linear measures are all equal. The scale factor is 2:3.

ANSWER

The prisms are not similar because the ratios of corresponding linear measures are not all equal.

ANSWER

a. Lengths48 Widths

24 Heights

22

b. Lengths 46 Widths

23 Heights

23

12

= 12= 1

1=

23=

GUIDED PRACTICE for Example 1

Tell whether the pair of right solids is similar. Explain your reasoning.

1.

GUIDED PRACTICE for Example 1

SOLUTION

The solids are similar because the ratios of corresponding sides is in the ratio 4:3

ANSWER

43=Lengths

1612

43=Lengths

129

Ratio

• What is the pattern?• Side:• Surface Area:• Volume:

Formula

EXAMPLE 3 Find the scale factor

The pyramids are similar. Pyramid P has a volume of 1000 cubic inches and Pyramid Q has a volume of 216 cubic inches. Find the scale factor of Pyramid P to Pyramid Q.

EXAMPLE 3 Find the scale factor

SOLUTION

Use Theorem 12.13 to find the ratio of the two volumes.

a3

b3 = 1000216

The scale factor of Pyramid P to Pyramid Q is 5:3.

ANSWER

Write ratio of volumes.

Find cube roots.

Simplify.

ab = 6

10

ab = 5

3

GUIDED PRACTICE for Examples 2, 3, and 4

Cube C has a surface area of 54 square units and Cube D has a surface area of 150 square units. Find the scale factor of C to D. Find the edge length of C, and use the scale factor to find the volume of D.

3.

SOLUTION

a2

b2 = 54150 Write ratio of volumes.

Find square roots.

Simplify.

ab = 5

3

ab = 3

5

Use Theorem 12.13 to find the ratio of the two properties.

GUIDED PRACTICE for Examples 2, 3, and 4

C edgeD edge = 3

5 Use Scale Factor.

Find the edge length.

Surface area = 54 square units

Single side = 9 units

Edge length = 3 units

Find volume of D

D edge = 5

Volume of D = 125 square units

Homework

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