 # 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.

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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. Lengths 4 8 Widths 2 4 Heights 2 2 b. Lengths 4 6 Widths 2 3 Heights 2 3 1 2 = 1 2 = 1 1 = 2 3 =

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 4 3 = Lengths 16 12 4 3 = Lengths 12 9

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. a3a3 b3b3 = 1000 216 The scale factor of Pyramid P to Pyramid Q is 5:3. ANSWER Write ratio of volumes. Find cube roots. Simplify. a b = 6 10 a b = 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 a2a2 b2b2 = 54 150 Write ratio of volumes. Find square roots. Simplify. a b = 5 3 a b = 3 5 Use Theorem 12.13 to find the ratio of the two properties.

GUIDED PRACTICE for Examples 2, 3, and 4 C edge D 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 Page 850-851 – # 3- 21 odd

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