Question 287598
A right circular cylinder is given. If the radius is increased by 25% then the volume will stay the same if the height is increased/decreased by what percent? 
(a) Increased by 64% (b) Decreased by 36% (c) Decreased by 25% 
(d) Increased by 25% (e) None of the above

Let r be the original radius, h the original height and H the new increased height.  Then we have:

1.) volume of original cylinder = pi*(r^2)*h
2.) volume of cylinder with increased radius = pi*(1.25r)^2*H

For the volume not to change we must have:

pi*(r^2)*h = pi*(5/4*r)^2*H
pi*(r^2)*h = pi*25/16*r^2*H

Divide both sides above by pi:

r^2*h = (25/16)*r^2*H

Divide both sides by r^2:

h = (25/16)*H
H = (16/25)*h
H = .64*h

The height must be DECREASED by .36, that is 36%.