Chapter 12.8, Problem 14PPS

To determine

Find the volume of the other prism.

Answer to Problem 14PPS

  $\text{101}{\text{.25yard}}^3$

Explanation of Solution

Given:

Two rectangular prisms are similar.The height of the first prism is 6 yards and the height of the other prism is 9 feet.The volume of the first prism is 810 cubic yards.

Formula Used: If the ratio of the sides of two similar solids is a : b , then the ratio of the volume of the solids is

  $a^3:b^3$

  $1feet=\frac{1}{3}yard$

Calculation:

Height of the second prism = 9 feet = $\frac{9}{3}=3yards$

Ratio of heights of the prisms is

  $\frac{6}{3}=\frac{2}{1}$

= 2:1

So, the ratio of the volumes of the prisms is

  $2^3:1^3=8:1$

Let volume of the other prism is V cubic yard

  $\begin{array}{l}\Rightarrow \frac{810}{V}=\frac{8}{1}\\ \Rightarrow 810=8V\mathrm{...............}[\text{multiply each side by V]}\\ \Rightarrow \text{V=}\frac{810}{8}\mathrm{.................}[\text{divide each side by 8]}\\ \Rightarrow \text{V=101}{\text{.25yard}}^3\end{array}$