Question

A right circular cylinder and a right circular cone have the same base radius and same height. What is the ratio of the volume of the cylinder to that of cone?

Solution

Let V and ‘R’ be the radii of cylinder and cone respectively.
And ‘h’ and ‘H’ be the heights of cylinder and cone respectively.
Now volume of cylinder (v₁) = $πr squared straight h$
And, volume of cone (v₂) = $1 third space πr squared straight h$
$Now comma space space space space straight v subscript 1 over straight v subscript 2 equals fraction numerator πr squared straight h over denominator begin display style 1 third end style πR squared straight H end fraction space space space space space space space space space space space space space space space space equals space fraction numerator πr squared straight h over denominator begin display style 1 third end style πr squared straight h end fraction space left square bracket because space straight r space equals space straight R comma space straight h space equals space straight H right square bracket space space space space space space space space space space space space space space space space space equals space fraction numerator 1 over denominator begin display style 1 third end style end fraction equals 3 over 1$