Chapter 12.6, Problem 55SPR

To determine

Calculate the volume of the pyramid.

Answer to Problem 55SPR

The volume of the pyramid is $232.4m^3$ .

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 the base area.

  $\begin{array}{l}B=l\cdot w\\ B=(10)\cdot (6)\\ B=60\end{array}$

Now, to find height, use the Pythagoras theorem,

  $\begin{array}{l}{12}^2=3^2+h^2\\ 144=9+h^2\\ h^2=144-9\\ h^2=135\\ h=3\sqrt{15}\end{array}$

Now, the volume of the pyramid is

  $\begin{array}{l}V=\frac{1}{3}B{h}_{pyramid}\\ V=\frac{1}{3}(60)(3\sqrt{15})\\ V=60\sqrt{15}\\ V=232.4m^3\end{array}$

Conclusion:

The volume is $232.4m^3$ .