The Circumference of the circular ends of a frustum are 48cm and 36 cm. if the height of the frustum is 11 cm , find its volume. ( Take π = 22/7)

We know that, Circumference of a circle $=2\pi r$

Let radius of Larger end of frustum $=R$

Let radius of smaller end of frustum $=r$

Circumference of Larger end $=2\pi R=48 \mathrm{cm}$

 So, $R=48/2\pi =24/\pi$ Perimeter of Smaller end $=2\pi r$$=36 \text{cm}$

$=36 \mathrm{cm}$

$\mathrm{So},r=36/2\pi =18/\pi$

We know that, Volume of the frustum $=1/3\pi \text{h}\left({\text{R}}^2+{\text{r}}^2+\text{Rr}\right)$,

$=1/3\pi \mathrm{h}\left({\mathrm{R}}^2+{\mathrm{r}}^2+\mathrm{Rr}\right)\mathrm{h}=11 \mathrm{cm},$

$\mathrm{R}=24/\pi$

$r=18/\pi V$

$=1/3\times \pi \times 11\left({(24/\pi )}^2+{(18/\pi )}^2+24/\pi \times 18/\pi \right)$

$=11/3\pi (576+324+432)$

$=11/3\times \left(1332\right)\times 7/22$

$=1554 {\text{cm}}^3$