Question : The ratio of radii of a cylinder to a cone is 3 : 1. If their heights are equal, What is the ratio of their volumes?
Option 1: 1 : 3
Option 2: 27 : 1
Option 3: 9 : 1
Option 4: 1 : 9
Correct Answer: 27 : 1
Solution :
Given: The ratio of radii of a cylinder to a cone is 3 : 1.
Let the radii of the cylinder and the cone be 3$r$ and $r$.
Let the heights of the cylinder and the cone be $h$.
Now, the volume of the cylinder = $\pi (3r)^2h$ = $9\pi r^2h$
and the volume of the cone = $\frac{1}{3}\pi r^2h$
So, the required ratio of their volumes
= $9\pi r^2h$ : $\frac{1}{3}\pi r^2h$
= 27 : 1
Hence, the correct answer is 27 : 1.
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