Chapter 12.5, Problem 2CYU

To determine

To find the volume of the given pentagonal pyramid.

Answer to Problem 2CYU

  $V=133.24$ cubic centimeters (approximately)

Explanation of Solution

Given:

  

Height, ( $h$ ) $=12$ centimeters

Side of the pentagonal base ( $a$ ) $=4.4$ 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 pentagon $=\frac{1}{4}\sqrt{5(5+2\sqrt{5})}{a}^2$ where a is the side of the pentagon.

Calculation:

Area of the pentagon, ( $B$ ) $=\frac{1}{4}\sqrt{5(5+2\sqrt{5})}{a}^2$ ,

Putting $a=4.4$ in the above formula,

  $\Rightarrow B=\frac{1}{4}\sqrt{5(5+2\sqrt{5})}{(4.4)}^2$

  $\Rightarrow B\approx 33.31$ square centimeters.

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

Now put the values of $B=33.31$ and $h=12$ ,

  $\Rightarrow \frac{1}{3}\times 33.31\times 12$

  $\Rightarrow \frac{399.72}{3}$

  $\Rightarrow V\approx 133.24$ cubic centimeters (approximately)

Conclusion:

Therefore, the volume of the given pentagonal pyramid is $133.24$ cubic centimeters (approximately).