A coffee company decides to increase the diameter of their cylindrical coffee cans to make the can more appealing to consumers. If the diameter of the can is increased by , by what percent will the height be decreased if the volume remains the same?
Source: mathcontest.olemiss.edu 4/8/2013
Let be the radius of the original coffee can and its height.
Volume of original can
Let be the radius of the new can and its height. If the diameter of the original can is increased by , then its radius is also increased by the same amount.
Volume of new can
Volume remains the same
The new height is of the original height or the original height has decreased by .