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?

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.