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Lesson 9-5

Lesson 9-5. Similar Solids. Two solids of the same type with equal ratios of corresponding linear measures (such as heights or radii) are called similar solids. Similar Solids. Similar solids. NOT similar solids. Similar Solids. 4. 6. 2. 8. 3. 12.

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Lesson 9-5

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  1. Lesson 9-5 Similar Solids Lesson 9-5: Similar Solids

  2. Two solids of the same type with equal ratios of corresponding linear measures (such as heights or radii) are called similar solids. Similar Solids Lesson 9-5: Similar Solids

  3. Similar solids NOT similar solids Similar Solids Lesson 9-5: Similar Solids

  4. 4 6 2 8 3 12 Similar Solids & Corresponding Linear Measures To compare the ratios of corresponding side or other linear lengths, write the ratios as fractions in simplest terms. Length: 12 = 3 width: 3 height: 6 = 3 8 2 2 4 2 Notice that all ratios for corresponding measures are equal in similar solids. The reduced ratio is called the “scale factor”. Lesson 9-5: Similar Solids

  5. 9 12 6 12 8 16 Example: Are these solids similar? Solution: All corresponding ratios are equal, so the figures are similar Lesson 9-5: Similar Solids

  6. 18 6 4 8 Example: Are these solids similar? Solution: Corresponding ratios are not equal, so the figures are not similar. Lesson 9-5: Similar Solids

  7. Scale Factor and Area What happens to the area when the lengths of the sides of a rectangle are doubled? Ratio of sides = 1: 2 Ratio of areas = 1: 4 What is the scale factor for the two rectangles? The ratio of the areas can be written as 1: 2 12: 22 Lesson 9-5: Similar Solids

  8. 8 6 6 Similar Solids and Ratios of Areas • If two similar solids have a scale factor of a : b, then corresponding areas have a ratio of a2: b2. • This applies to lateral area, surface area, or base area. Ratio of sides = 3: 2 12 9 9 Surface Area = B + L.A. = 6(6) + (6 + 6 + 6 + 6)(8)/2 = 36 + 96 = 132 Surface Area = B + L.A. = 9(9) + (9 + 9 + 9 + 9)(12)/2 = 81 +216 = 297 Ratio of surface areas: 297:132 = 9:4 = 32: 22

  9. Scale Factor and Volume What happens to the surface area and volume when the lengths of the sides of a prism are doubled? Ratio of sides = 1: 2 Ratio of areas = 1: 4 Ratio of volumes = 1: 8 1: 2 The scale factor for the two prisms is The ratio of the surface areas can be written as The ratio of the volumes can be written as 12: 22 13: 23 Lesson 9-5: Similar Solids

  10. 9 6 15 10 Similar Solids and Ratios of Volumes • If two similar solids have a scale factor of a : b, then their volumes have a ratio of a3 : b3. Ratio of heights = 3:2 V = r2h =  (92) (15) = 1215  V= r2h = (62)(10) = 360  Ratio of volumes: 1215: 360 = 27:8 = 33: 23 Lesson 9-5: Similar Solids

  11. 18 m 6 m Example 1: These two solids are similar. • The scale factor is • The ratio of areas is • The ratio of volumes is 18: 6 = 3: 1 182: 62 = 32: 12 = 9:1 183: 63 = 33: 13 = 27:1 Lesson 9-5: Similar Solids

  12. 18 m 6 m Example 2: These two solids are similar. If the radius of the larger cone is 6 m, what is the radius of the smaller cone? Solution: Write a proportion. Lesson 9-5: Similar Solids

  13. 18 m 6 m Example 3: These two solids are similar. If the lateral area of the smaller cone is 12, what is the lateral area of the larger cone? Solution: Write a proportion. Use ratio of AREAS. Lesson 9-5: Similar Solids

  14. 18 m 6 m Volume of larger is 27 times volume of smaller! Example 4: These two solids are similar. If the volume of the larger cone is 96 , what is the volume of the smaller cone? Solution: Write a proportion. Use ratio of VOLUMES. Lesson 9-5: Similar Solids

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