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A cylindrical tin can holding 2 gal. has its height equal to the diameter of its base.

Another cylindrical tin can with the same capacity has its height equal to twice the diameter of its base.

Find the ratio required for making the two can with covers.

The shorter can has radius and height

Its volume is: .

The taller can has radius and height

Its volume is: .

The volumes are equal: . .[1]

The short can has surface area: .

The tall can has surface area: .

Ratio: .

Substitute [1]: .