Chapter 12.5, Problem 12PPS

To determine

To find the volume of the given rectangular pyramid.

Answer to Problem 12PPS

  $V=482.08$ cubic meters

Explanation of Solution

Given:

  

Height ( $h$ ) $=12$ meters

Rectangular base:

Length $=13.1$ meters

Breadth $=9.2$ meters

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.

Area of a rectangle $=Length\times Breadth$

Calculation:

Since the given pyramid is a rectangular pyramid, so it has a rectangularbase.

So, area of the base, $B=\text{Length}\times \text{Breadth}$

  $\Rightarrow B=13.1\times 9.2$

  $\Rightarrow B=120.52$ square meters

Now for the volume ( $V$ ) of the pyramid,

  $V=\frac{1}{3}Bh$

Now put the values of $B=120.52$ and $h=12$ ,

  $\Rightarrow \frac{1}{3}\times 120.52\times 12$

  $\Rightarrow \frac{1446.24}{3}$

  $\Rightarrow V=482.08$ cubic meters

Conclusion:

Therefore, the volume of the given rectangular pyramid is $482.08$ cubic meters.