If the diameter of a right cylindrical can with circular bases is increased by 25%, by what percent should the height be decreased in order to preserve the volume of the original can?
+129907 Call the volume of the original can pi * r^2 * h
If the diameter is increased by 25 % then so is the radius
So we want to know this
pi * r^2 * h = pi * (1.25 r)^2 (1 - a) * h where a is the % of height decrease
1 = 1.5625 (1 - a)
1/ 1.5625 = ( 1 - a) =
.64 = 1 - a rearrange as
a = 1 - .64 = .36 ......the height should be decreased by 36%
