Question

the ratio of the radii of two cons having equal height is 2:3. then ,the ratio of their volumes=____________
(a) 4:6 (b) 8:27 (c) 3:2 (d) 4:9

Answer 1

Since the radii are in the ratio 2:3 they can be taken as 2r and 3r units respectively.

Since it is given that both cylinders have same height, let it be h units

Volume of a cylinder is πr^2 h

Ratio of volumes = π (2x)^2h/π (3x)^2 h

= π 4x^2 h/π 9h^2 h = 4:9

So ratio of volumes 4:9

Conclusion: Ratio of volumes of cylinders is as the ratio of square of the radii if the height remains the same.