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Q20.

Expert-verified

Geometry

Found in: Page 486

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

A pyramid and a prism both have height 8.2 cm and congruent hexagonal bases with area 22.3 cm². Give the ratio of their volumes.

The ratio of volumes of pyramid and prism is $\frac{1}{3} : 1$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Pyramid and prism height is 8.2 cm and congruent hexagonal bases with area 22.3 cm².

Step 2. Determine the ratio.

to find the ration of the volumes, divide the volumes of pyramid and prism,

Thus, the ratio of volumes of pyramid and prism is . $\begin{array}{l} \frac{v_{p y}}{v_{p r}} = \frac{\frac{1}{3} b h}{b h} \\ \frac{v_{p y}}{v_{p r}} = \frac{\frac{1}{3} (22.3) (8.2)}{(22.3) (8.2)} [substitute] \\ \frac{v_{p y}}{v_{p r}} = \frac{\frac{1}{3}}{1} [divide out common factor] \end{array}$

Thus, the ratio of volumes of pyramid and prism is $\frac{1}{3} : 1$ .

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