1. 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?

2. Exploring Similar Solids 12.7

3. What is similar

4. 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.

5. 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 =

6. GUIDED PRACTICE for Example 1 Tell whether the pair of right solids is similar. Explain your reasoning. 1.

7. 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

8. Ratio What is the pattern? Side: Surface Area: Volume:

9. Formula

10. 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.

11. 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

12. 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.

13. 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

14. Homework Page 850-851 – # 3- 21 odd