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Surface Area & Volume

Lesson 23. Surface Area & Volume. Similar Solids. Warm-Up. Draw and label two circles that are similar. Identify their scale factor. Draw two rectangles that are similar. Identify their scale factor.   ∆ABC is similar to ∆ XYZ. Use a proportion to solve for x. 6. 4. 12. x.

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Surface Area & Volume

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  1. Lesson 23 Surface Area & Volume Similar Solids

  2. Warm-Up • Draw and label two circles that are similar. Identify their scale factor. • Draw two rectangles that are similar. Identify their scale factor.   • ∆ABC is similar to ∆ XYZ. Use a proportion to solve for x. 6 4 12 x

  3. Similar Solids Target: Use ratios and proportions when finding scale factors, linear ratios, area ratios and volume ratios of similar solids.

  4. Vocabulary • Similar Solids: Solids with the same shape and all corresponding dimensions are proportional.

  5. Similar Solids If two solids are similar then: • Their linear ratio (scale factor) is a : b. • The ratio of their areas is a2 : b2. • The ratio of their volumes is a3 : b3.

  6. Example 1 Are the cylinders similar? • Find the ratio of the radii. • Find the ratio of the heights then simplify. • Cylinders are similar if their radii and heights have the same ratio. • Cylinder A and B are similar.

  7. Example 2 Two solids have a scale factor 3 : 4. a. Find their area ratio. • Square the scale factor. 32 : 42 → 9 : 16 b. Find the volume ratio. • Raise the scale factor to the third power. 33 : 43 → 27 : 64

  8. Example 3 Two children each have an ice cream cone. The ice cream cones are similar in shape, but one is larger than the other. The cones have a scale factor of 2:5. The volume of the small cone is 121.4 cm3. Find the volume of the larger cone. • Find the volume ratio. a3 : b3 → 23 : 53 → 8 : 125 → • Write a proportion using the volume ratio. • Set the cross products equal. 8x = 15175 • Divide both sides by 8. 8 8 • The volume of the cone is 1,896.875 cm3.

  9. Exit Problems • Two similar solids have an area ratio of 4² : 9². • Identify the ratio of the linear measures. • Identify the ratio of the volumes. • What is the scale factor between the solids? • Two cylinders have a scale factor of 2 : 7. The surface area of the large cylinder is 595 square inches. Find the surface area of the smaller cylinder. Round to the nearest hundredth.

  10. Communication Prompt • Jeremy was told the scale factor between two solids was 4 : 7. What additional conclusions can Jeremy make about the solids? • When and where is volume used in daily life?

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