Chapter 12.5, Problem 13PPS

To determine

To find the volume of the given hexagonal pyramid.

Answer to Problem 13PPS

  $V=230$ cubic centimeters (approximately)

Explanation of Solution

Given:

  

Height, ( $h$ ) $=7.5$ centimeters

Hexagonal base:

Side, ( $a$ ) $=6$ 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 hexagon $=\frac{3\sqrt{3}}{2}{a}^2$ where $a$ is measure of the side of the hexagon.

Calculation:

Since the given pyramid is a hexagonal pyramid, so it has a hexagonal base.

So, area of the base, $B=\frac{3\sqrt{3}}{2}{a}^2$ ,

  $\Rightarrow B=\frac{3\sqrt{3}}{2}{(6)}^2$

  $\Rightarrow \frac{187.061487}{2}$

  $\Rightarrow B\approx 93.53$ square centimeters

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

  $V=\frac{1}{3}Bh$

Now put the values of $B=93.53$ and $h=7.5$ ,

  $\Rightarrow \frac{1}{3}\times 93.53\times 7.5$

  $\Rightarrow \frac{701.475}{3}$

  $\Rightarrow V\approx 230$ cubic centimeters

Conclusion:

Therefore, the volume of the given hexagonal pyramid is $230$ cubic inches (approximately).