Chapter 12.2, Problem 6CE

To determine

To find: The volume of given pyramid.

Answer to Problem 6CE

The volume of given pyramid is $384{\text{ unit}}^3.$

Explanation of Solution

Given information:

V-ABCD is a regular square pyramid.

  

Calculation:

Since, the pyramid has a square base ABCD .

  $\text{AB}=\text{BC}=12$

Calculate area of base of pyramid.

  $\begin{array}{l}\text{Area of base}=12\times 12\\ =144{\text{ unit}}^2\end{array}$

From figure, the height of pyramid $h=8$ .

Calculate volume of pyramid.

  $\begin{array}{l}\text{Volume of pyramid}=\frac{1}{3}\times \text{height}\times \text{area of base}\\ \text{ =}\frac{1}{3}\times 8\times 144\\ =48\times 8\\ =384{\text{ unit}}^3\end{array}$

Therefore, the volume of given pyramid is $384{\text{ unit}}^3.$