Chapter 12, Problem 24SGR

To determine

To find the volume of the given regular square pyramid.

Answer to Problem 24SGR

  $V=18$ cubic centimeters

Explanation of Solution

Given:

  

Height ( $h$ ) $=6$ centimeters, side of the base $=3$ 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 square $={(side)}^2$

Calculation:

Since the given pyramid is a square pyramid, so it has a squarebase.

So, $B={(side)}^2$

  $\Rightarrow B={(3)}^2$

  $\Rightarrow B=9$ square centimeters

Now for the volume ( $V$ ) of the pyramid, use the below formula.

  $\Rightarrow V=\frac{1}{3}Bh$

Now put the values of $B=9$ and $h=6$ ,

  $\Rightarrow \frac{1}{3}\times 9\times 6$

  $\Rightarrow 18$

  $\Rightarrow V=18$ cubic centimeters

Conclusion:

Therefore, the volume of the given square pyramid is $18$ cubic centimeters.