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Question
The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. Calculate the ratio of their volumes.
Solution
Here, r1 = Radius of cylinder 1
h1 = Height of cylinder 1
r2 = Radius of cylinder 2
h2 = Height of cylinder 2
V1 = Volume of cylinder 1
V2 = Volume of cylinder 2
Ratio of the radii of two cylinders = 2:3
Ratio of the heights of two cylinders = 5:3
Volume of the cylinder = πr2h
V1/V2 = (πr12h1)/(πr22h2) = (π(2r)25h)/(π(3r)23h)
V1/V2 = (π4r25h)/(π9r23h) = 20 / 27
Hence, the ratio of their volumes is 20:27
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