The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3.

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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