Question

The perimeters of the ends of a frustum are $48cm$ and $36cm$. If the height of the frustum be $11cm$, find its volume.

Answer 1

Let $r_1$ and $r_2$ be the radii of the circular ends of the frustum and $h$ be its height.

Then,
$2\pi r_1=48,2\pi r_2=36;h=11cm\Rightarrow r_1=\frac{24}{\pi },r_2=\frac{18}{\pi };h=11cm$

Let $V$ be the volume of the frustum. Then

$V=\frac{1}{3}\pi (r_1^2+r_2^2+r_1{r}_2)h$

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

$\Rightarrow V=\frac{1}{3}\times \pi \times 11\times \frac{576+324+432}{{\pi }^2}{cm}^3=\frac{11}{3}\times \frac{1332}{22}\times 7{cm}^3=1554{cm}^3$