Question

A conical dome of a palace is supported by a cylindrical pillar, both having the same radius. If the ratio of heights of cylinder to cone is $4:3,$ then the ratio of their volumes is

• A. 2:1
• B. 3:1
• C. 4:1
• D. 1:1

Answer 1

The correct option is C

4:1

Since, the ratio of the heights of the cylinder to cone is $4:3$,

let height of cylinder, $h_{\text{cylinder}}$ be $4x$ and height of cone, $h_{\text{cone}}$ be $3x$

$\Rightarrow$ Ratio of volumes $=\frac{\pi r^2{h}_{\text{cylinder}}}{\frac{1}{3}\pi r^2{h}_{\text{cone}}}$

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

$=4:1$