Question

A cylinder’s radius is reduced to two-fifths its original size and the height is quadrupled. How has the volume of the cylinder changed?

Answer 1

Let the original volume be pi *r^2* h where  r = radius and h = height.

The new volume will be pi *(2/5 r)^2 * 4h  =  pi*4/25 r^2 4h

pi*4/25r^2 * 4h  /  pi r^2 h  = 4/25 * 4 = 16/25

The volume has been reduced  by  factor of 16/25.