If the radius of the base of a right circular cylinder is halved, keeping the height same, what is the ratio of the volume of the reduce cylinder to that of the original.

Explanation

Original radius `r_1=r`
Reduced radius `r_2=r/2`
The ratio of the volume of the reduced cylinder to that of the original:
Volume of the reduced cylinder`/`Volume of the original cylinder
`=(pi(r/2)^2h)/(pir^2h)=(pir^2/4^2h)/(pir^2h)=1/4`
`therefore` The ratio of the volume of the reduced cylinder to that of the original`=1/4`