Math CentralQuandaries & Queries


Question from Scott, a teacher:

a cylindrical tin is 15 inches high and holds 5 gallons of paint when it is full. Find the diameter of the tin.
(1 gallon = 0.1605 cubic feet)

Hi Scott,

The volume of a cylinder is the area of the base times the height. The base of your cylinder is a circle of unknown radius $r$ feet and height $h = 15/12$ feet and the area of a circle of radius $r$ feet is $\pi \; r^2$ square feet.

Your cylinder has a known volume of 5 gallons and one gallon is 0.1605 cubic feet. Putting this all together you have

\[\pi \; r^2 \times \frac{15}{12} = 5 \times 0.1605 \mbox{ cubic feet.}\]

Solve for $r.$


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