Chapter 12.2, Problem 12PPS

To determine

To find: the volume of the prism

Answer to Problem 12PPS

Thevolume of the prismis $868{\text{ yd}}^3$ .

Explanation of Solution

Given:

The base of the triangle is $6.2\text{ yd}$

Height of the triangle is $\text{20 yd}$

The height of the prism is $\text{14 yd}$ .

Formula used:

The volume Vof the prism is $V=Bh$

Calculation:

The objective is to find the volume of the prism.

The volume V is given by the formula

  $V=Bh$

Where B is the area of a face and h is the height of the prism.

From the figure the area B is a triangle whose base is $6.2\text{ yd}$ and height is $\text{20 yd}$ .

The area B of the triangle is given by

  $\begin{array}{l}B=\frac{1}{2}\cdot b\cdot a\text{ Where }a\text{ is a triangle whose base is 602 yd and height is 20 yd}\\ \text{=}\frac{1}{2}\cdot \left(6.2\right)20\\ =\left(6.2\right)10\\ =62\end{array}$

Put $B=62$ and $h=14$ in the volume formula to find the volume.

Thus, the volume V is

  $\begin{array}{l}V=Bh\\ =62\cdot 14\\ =868{\text{ yd}}^3\end{array}$

Conclusion:

Therefore, thevolume of the prism is $868{\text{ yd}}^3$ .