Chapter 12.4, Problem 14PPS

To determine

To find:

The volume of the prism.

Answer to Problem 14PPS

The volume of the prism is ${\text{2040 cm}}^3$ .

Explanation of Solution

Given information:

An oblique hexagonal prism with a height of $15\text{ cm}$ and with a base area of ${\text{136 cm}}^2$ .

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 $B=136$ and $h=15$ in the above formula:

  $\begin{array}{c}V=136\left(15\right)\\ =2040{\text{ cm}}^3\end{array}$

Hence the volume of the prism is ${\text{2040 cm}}^3$ .