Q6. - Geometry

Question

V- ABCD is a regular square pyramid. Find the following numerical answers.

$\text{Volume}=\_\_\_$

Step-by-Step Solution

Answer

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

Step 1. Given information.

The given$V-ABCD$ is a regular square pyramid.

Also,$AB=12$ and $BC=12$.

Step 2. Determine the area.

The edge length of square base is 12 and height of pyramid is 8.

Calculate area of base of pyramid.

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

Step 3. Determine the volume.

In $\Delta VBC$, calculate the area.

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

 

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