Coffee Can

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 25\%, by what percent will the height be decreased if the volume remains the same?
Source: mathcontest.olemiss.edu 4/8/2013

SOLUTION
Let r be the radius of the original coffee can and h its height.
Volume of original can
V=\pi r^2h
Let r' be the radius of the new can and h' its height. If the diameter of the original can is increased by 25\%, then its radius is also increased by the same amount.
r'=r+\left (25\%\right )r
=r\left (1+.25\right )
=1.25r
Volume of new can
V'=\pi\left (r'\right )^2h'
=\pi\left (1.25r\right )^2h'
=1.5625\pi r^2h'
Volume remains the same
\pi r^2h=1.5625\pi r^2h'
Simplify
h=1.5625h'
h'=.64h
=(64\%)h
The new height is 64\% of the original height or the original height has decreased by 36\%.

Answer: 36\%

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About mvtrinh

Retired high school math teacher.
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