Question

If the volume of the cone is 66 $i{n}^3$ and the diameter is 6 in, then what is the height of the cone? $(\text{use}\pi =\frac{22}{7})$

Answer 1

Given:
Volume of the cone $=66{\text{in}}^3$
Diameter of the cone $=6\text{in}$
$\Rightarrow$ Radius of the cone $\left(r\right)=\frac{\text{Diameter}}{2}=3\text{in}$

Let the height of the cone be $“h”$.
We know that the volume of the cone $=\frac{1}{3}\pi r^{2}h$

$\Rightarrow \frac{1}{3}\pi r^{2}h=66$ (equating with the formula for volume)
$\Rightarrow \frac{1}{3}\times \frac{22}{7}\times 3^2\times h=66$ (substituting for r and $\pi$)
$\Rightarrow h=\frac{66\times 3\times 7}{3\times 3\times 22}$ (transposing $\frac{22}{7}$ and $3^2$ to R.H.S.)
$\Rightarrow h=7\text{inches}$
Therefore, the height of the cone is 7 inches.
$\to$Option A is correct.