Chapter 12.5, Problem 11PPS

To determine

To find the volume of the given triangular pyramid.

Answer to Problem 11PPS

  $V=109.47$ cubic millimeters

Explanation of Solution

Given:

  

Height ( $h$ ) $=8.6$ millimeters

Triangular base:

Height $=8.2$ millimeters

Base $=9$ millimeters

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 triangle $=\frac{1}{2}\times Base\times Height$

Calculation:

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

So, area of the base, $B=\frac{1}{2}\times \text{Base}\times \text{Height}$

  $\Rightarrow B=\frac{1}{2}\times 9\times 8.2$

  $\Rightarrow B=36.9$ square millimeters

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

  $V=\frac{1}{3}Bh$

Now put the values of $B=36.9$ and $h=8.6$ ,

  $\Rightarrow \frac{1}{3}\times 36.9\times 8.6$

  $\Rightarrow \frac{328.41}{3}$

  $\Rightarrow V=109.47$ cubic millimeters

Conclusion:

Therefore, the volume of the given square is $109.47$ cubic millimeters.