Question

The radius of the base of a cone is $6$ inches. What is its volume if its height is $4$ inches?

Answer 1

Detailed step-by-step solution:
The radius of the base of the cone, $r=6$ inches
Height of the cone, $h=4$ inches




Volume of the cone is ${\frac{1}{3}}^{\text{rd}}$ of the volume of the cylinder with equal base and equal height.
Volume of the cone $=\frac{1}{3}$ Base area $\times$ Height (writing the formula for volume)
$=\frac{1}{3}\left(\pi r^{2}h\right)$
$=\frac{1}{3}\times (\pi \times 6^2\times 4)$ (substituting the values)
$=\frac{1}{3}\times (\pi \times 36\times 4)$
$=\frac{144}{3}\pi$ (simplifying)
$=48\pi$ cubic inches
$\Rightarrow$ Option A is correct.