Question

Find the ratio of volumes of a cone and a cylinder whose heights are same but radius of the cone is 3 times that of the cylinder.

• A. $1:3$
• B. $9:1$
• C. $3:1$
• D. $1:9$

Answer 1

The correct option is C $3:1$

$\text{Volume of a cone}=\frac{1}{3}\pi r^{2}h$
[r = Radius; h = Height]

$\text{Volume of a cylinder}=\pi r^{2}h$
[r = Radius; h = Height]

Let the height be 'h' and the radius of the cylinder be 'r'.
Then, the radius of the cone = 3r

$\text{Volume of the cone}=\frac{1}{3}\pi (3r{)}^{2}h=3\pi r^{2}h$
$\text{Volume of the cylinder}=\pi r^{2}h$

$\text{Ratio}=3\pi r^{2}h$:$\pi r^{2}h$ = 3:1