Question

The ratio of the volumes of a right circular cylinder and a right circular cone of the same base and the same height will be:

• A. $1:3$
• B. $4:3$
• C. $3:1$
• D. $3:4$

Answer 1

The correct option is C

$3:1$

Finding ratio of volumes of cylinder and cone

The volume of right circular cylinder $\left(v\right)$$={\mathrm{\pi r}}^2\mathrm{h}$

The volume of right circular cone $\left(V\right)$$=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}$

The radii and height of the cylinder and cone is same.

Ratio of right circular cylinder and right circular cone is given by:

$v:V={\mathrm{\pi r}}^2\mathrm{h}:\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}$

$\Rightarrow \frac{v}{V}=\frac{{\mathrm{\pi r}}^2\mathrm{h}}{{\displaystyle \frac{1}{3}}{\mathrm{\pi r}}^2\mathrm{h}}$

$\Rightarrow \frac{v}{V}=\frac{1}{{\displaystyle \frac{1}{3}}}$

$\Rightarrow \frac{v}{V}=\frac{3}{1}$

Therefore, the ratio of right circular cylinder and a right circular cone is $3:1$

Hence, option c is the correct answer.