Chapter 12.4, Problem 15PPS

To determine

To find:

The volume of the prism.

Answer to Problem 15PPS

The volume of the prism is $\text{1534}{\text{.25 in}}^3$ .

Explanation of Solution

Given information:

A square prism with a base edge of $9.5$ inches and a height of $17$ inches.

Calculation:

The volume $V$ of a prism is $V=Bh$ , where $B$ is the area of a base and $h$ is the height of the prism.

If two solids have the same height $h$ and the same cross-sectional area $B$ at every level, then they have the same volume. So, the volume of a right prism and an oblique one of the same height and cross sectional area are same

Substitute $B={\left(9.5\right)}^2$ and $h=17$ in the above formula:

  $\begin{array}{c}V={\left(9.5\right)}^2\left(17\right)\\ =1534.25{\text{ in}}^3\end{array}$

Hence the volume of the prism is $\text{1534}{\text{.25 in}}^3$ .