Chapter SH, Problem 8AAV

Solution

The exact volume of the given figure.

  $80000{\text{ ft}}^3$

Given:

The figure,

  

Concept Used:

The volume of a pyramid with height h is given by the formula, $V=\frac{1}{3}\cdot \left(\text{Area of base}\right)\cdot h$ .

Calculation:

In order to find the exact volume of the given rectangular pyramid, note that the height is 50 ft and the lengths of the base are 80 ft and 60 ft, so the volume of the rectangular pyramid is given by

  $\begin{array}{c}V=\frac{1}{3}\cdot \left(\text{Area of base}\right)\cdot h\\ =\frac{1}{3}\cdot \left(80\cdot 60\right)\cdot 50\\ =\frac{240000}{3}\\ =80000{\text{ ft}}^3\end{array}$

Thus, the volume of the given figure is $80000{\text{ ft}}^3$ .