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Q20.

Expert-verified
Found in: Page 486

### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

# 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 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 .$\begin{array}{l}\frac{{v}_{py}}{{v}_{pr}}=\frac{\frac{1}{3}bh}{bh}\\ \frac{{v}_{py}}{{v}_{pr}}=\frac{\frac{1}{3}\left(22.3\right)\left(8.2\right)}{\left(22.3\right)\left(8.2\right)}\text{[substitute]}\\ \frac{{v}_{py}}{{v}_{pr}}=\frac{\frac{1}{3}}{1}\text{[divide out common factor]}\end{array}$

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