Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 11 - Surface Area and Volume - 11-7 Areas and Volumes of Similar Solids - Practice and Problem-Solving Exercises: 37

Answer

similarity ratio = 5:8 ratio of surface area = 25:64

Work Step by Step

The similarity ratio is the cube root of the ratio of volumes. $$\sqrt[3] \frac{125}{512} = \frac{5}{8}$$ The ratio of surface areas is the similarity ratio squared. $$\frac{5^{2}}{8^{2}}= \frac{25}{64}$$
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