Chapter 12.5, Problem 17WE

To determine

To find: Thevolume of the larger pyramid.

Answer to Problem 17WE

The volume of the larger pyramid is $108{\text{ft}}^3$ .

Explanation of Solution

Given information:

The lateral surface areas of two similar pyramids are $8{\text{ft}}^2$ and $18{\text{ft}}^2$ . The volume of the smallerpyramidis $32{\text{ft}}^3$ .

Calculation:

Calculate the scale factor is the ratio of lateral areas.

  $\begin{array}{c}S=\sqrt{\frac{8}{18}}\\ =\sqrt{\frac{4}{9}}\\ =\frac{2}{3}\end{array}$

Volume is proportional to the cube of scale factor.

  $\begin{array}{c}\frac{\text{Total}\text{volume}\text{of the}\text{smaller}\text{pyramid}}{\text{Total}\text{volume}\text{of the}\text{larger}\text{pyramid}}={\left(\frac{2}{3}\right)}^3\\ \frac{32}{\text{Total}\text{volume}\text{of the}\text{larger}\text{pyramid}}=\left(\frac{8}{27}\right)\\ \text{Total}\text{volume}\text{of the}\text{larger}\text{pyramid}=\left(\frac{8}{27}\right)\times 32\\ =108{\text{ft}}^3\end{array}$

Therefore,the volume of the larger pyramidis $108{\text{ft}}^3$ .