Chapter 12.2, Problem 20WE

To determine

To find: the ratio of volumes of pyramid and prism.

Answer to Problem 20WE

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

Explanation of Solution

Given information:

Pyramid and prism height is $8.2\text{cm}$ and congruent hexagonal bases with area $\text{22}{\text{.3cm}}^2$ .

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

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

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