Chapter 12.5, Problem 14PPS

To determine

To find the volume of the given pentagonal pyramid.

Answer to Problem 14PPS

  $V=1,380$ cubic feet (approximately)

Explanation of Solution

Given:

  

Height, ( $h$ ) $=7$ feet

Area of pentagonal base ( $B$ ) $=590$ square feet $$

Formula used:

Volume of pyramid, $V=\frac{1}{3}Bh$

where $B$ is the area of the base and $h$ is the height of the pyramid.

Calculation:

For the volume ( $V$ ) of the pyramid,$V=\frac{1}{3}Bh$

Now put the values of $B=590$ and $h=7$ ,

  $\Rightarrow \frac{1}{3}\times 590\times 7$

  $\Rightarrow \frac{4130}{3}$

  $\Rightarrow V\approx 1,380$ cubic feet

Conclusion:

Therefore, the volume of the given pentagonal pyramid is $1,380$ cubic feet (approximately).