Chapter 12.5, Problem 3CYP

To determine

To find the volume of the given rectangular pyramid.

Answer to Problem 3CYP

  $V=30,070$ cubic centimeters

Explanation of Solution

Given:

  

Height ( $h$ ) $=46$ centimeters

Rectangular base:

Length $=53$ centimeters

Breadth $=37$ centimeters

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 rectangular base.

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

  $\Rightarrow B=53\times 37$

  $\Rightarrow B=1,961$ square centimeters

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

  $V=\frac{1}{3}Bh$

Now put the values of $B=1961$ and $h=46$ ,

  $\Rightarrow \frac{1}{3}\times 1961\times 46$

  $\Rightarrow \frac{90206}{3}$

  $\Rightarrow V=30,070$ cubic centimeters (rounded to the nearest tenth)

Conclusion:

Therefore, the volume of the given rectangular pyramid is $30,070$ cubic centimeters.