The slant height of a cone is $25cm.$ If the circumference of the base of the cone is $44cm,$ then the volume of the cone is

A) $1052c{m}^3$

B) $2341.5c{m}^3$

C) $1232c{m}^3$

D) $3261c{m}^3$

The correct option is C: $1232c{m}^3$

Circumference of the base $=2\pi r,$ where ${}^{\prime }{r}^{\prime }$ is the radius of the base of the cone

$\Rightarrow 44=2\times \frac{22}{7}\times r$

$\therefore r=7cm$

Slant height, $l=\sqrt{r^2+h^2}=25cm$, ${}^{\prime }{h}^{\prime }$ is the height of the cone.

$h=\sqrt{{25}^2-7^2}=24cm$

Volume of the cone $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times \frac{22}{7}\times 7^2\times 24=1232c{m}^3$