If the radius of the base of a cone is halved, keeping the height same, what is the ratio of the volume of the reduced cone to that of the original.

Explanation

Let the radius and height of right circular cone
Then volume `V_1=pir^2h`
If radius becomes half of radius`=r/2 and height`=h`.
`Then volume `V_2=pi(r/2)^2h=(pir^2h)/4`
The ratio `V_1/V_2=(pir^2h)/((pir^2h)/4)=4/1`
Hence, the ratio is `4:1`.