Chapter 12.6, Problem 54SPR

To determine

Calculate the volume of the pyramid.

Answer to Problem 54SPR

The volume of the pyramid is $240i{n}^3$ .

Explanation of Solution

Given:

It is given in the question that the figure is shown below:

  

Concept Used:

In this, use the concept of pyramid and the volume be $V=\frac{1}{3}Bh$ .

Calculation:

Let’s find base side of the triangle to get base area, use the Pythagoras theorem,

  $\begin{array}{l}{17}^2=8^2+b^2\\ 289=64+b^2\\ b^2=289-64\\ b^2=225\\ b=15\end{array}$

Now find the base area.

  $\begin{array}{l}B=\frac{1}{2}b\cdot h_{traingle}\\ B=\frac{1}{2}(15)\cdot (8)\\ B=60\end{array}$

Now, the volume of the pyramid is

  $\begin{array}{l}V=\frac{1}{3}B{h}_{pyramid}\\ V=\frac{1}{3}(60)(12)\\ V=60\cdot 4\\ V=240i{n}^3\end{array}$

Conclusion:

The volume is $240i{n}^3$ .