Question

Find the volume of the given figure?

• A. $2\pi {\text{cm}}^3$
• B. $6\sqrt{7}\pi {\text{cm}}^3$
• C. $12\sqrt{7}\pi {\text{cm}}^3$
• D. $24\sqrt{7}\pi {\text{cm}}^3$

Answer 1

The correct option is B $6\sqrt{7}\pi {\text{cm}}^3$

Volume of the given figure = $2\times \frac{1}{3}\pi r^{2}h$.

$r$ is the radius of the cone

$h$ is the height of the cone

$l$ is the slant height of the cone

We know,

Height $h=\sqrt{l^2-r^2}=\sqrt{{\left(4\right)}^2-{\left(3\right)}^2}=\sqrt{7}\text{cm}$.

Therefore, Volume $=2\times \frac{1}{3}\times \pi \times 3\times 3\times \sqrt{7}=6\pi \sqrt{7}{\text{cm}}^3$.

Hence, option $B$ is correct.