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Understanding Similar Solids: Areas and Volumes

Learn to identify similar solids by comparing bases and lengths, and calculating scale factors. Discover how ratios of areas and volumes work with Theorem 12-11. Explore if all spheres, right cylinders, and cubes are similar.

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Understanding Similar Solids: Areas and Volumes

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  1. Section 12-5 Areas and Volumes of Similar Solids

  2. Similar solids • Solids that have the same shape but not necessarily the same size.

  3. How to tell if solids are similar: • Determine whether the bases are similar. • See if corresponding lengths are proportional. • Think Scale factor!

  4. Questions: • Are all spheres similar? • Are all right cylinders similar? • Are all cubes similar? Yes No Yes

  5. The ratio of the base areas, of the lateral areas, and of the total areas is • The ratio of the volumes is Theorem 12-11 • If the scale factor of two solids is , then • The ratio of corresponding perimeters is

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