Question

A conical dome of a palace is supported by a cylindrical pillar, both having the same radius. If the ratio of the height of the pillar to that of dome is 4:3, then what is the ratio of their volumes?

Answer 1

Given: the ratio of the height of the pillar to that of dome is 4:3 .

$\Rightarrow \frac{h_{cylinder}}{h_{cone}}=\frac{4}{3}$

We know that,
$volumeofcylinder=\pi r^{2}h$.
$volumeofcone=\frac{1}{3}\pi r^{2}h$.

Now, ratio of volume of cylinder to the volume of cone
$=\frac{\pi r^2{h}_{cylinder}}{\frac{1}{3}\pi r^2{h}_{cone}}$

$=\frac{\pi r^2\times 4}{\frac{1}{3}\pi r^2\times 3}$

$=\frac{4}{1}$

$=4:1$

Hence, the required ratio is $4:1$.