Chapter 12.2, Problem 15PPS

To determine

To find: the volume of the prism

Answer to Problem 15PPS

Theheight of the prismis $6\text{ yd}$ .

Explanation of Solution

Given:

Base of the triangle is $\text{10 yd}$

The base height of the prism is $\text{20 yd}$

The volume of the prism is ${\text{600 yd}}^3$ .

Formula used:

The volume Vof the prismis $V=Bh$

Calculation:

The objective is to find the height of the triangle.

Let a represent the height of the triangle.

The volume V is given by the formula

  $V=Bh$

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

The area B of the triangle is given by

  $\begin{array}{l}B=\frac{1}{2}\cdot b\cdot a\text{ Where }b\text{ is the base and }a\text{ is the height of the triangle}\\ \text{=}\frac{1}{2}\cdot 10\cdot a\\ =5a\end{array}$

Put $B=5a$ and $h=20$ in the volume formula to find the volume.

Thus, the volume V is

  $\begin{array}{l}V=Bh\\ 600=5a\cdot 20\\ =100a\\ 100a=600\left[\text{Arrange}\right]\\ a=\frac{600}{100}\left[\text{Divide both side by 100}\right]\\ =6\text{ yd}\end{array}$

Conclusion:

Therefore, theheight of the prism is $6\text{ yd}$ .