Question

Radii of base of cylinder and cone are in the ratio 3:4 and heights in ratio 2:3 . Find ratio of their volumes.

Answer 1

Radii of base of cylinder and cone are in the ratio 3:4 and heights in ratio 2:3 .
Let the radius of the cylinder be 3r, and radius of cone is 4r
Let the height of cylinder be 2h and height of the cone be 3h.

And the volume of the cylinder is given by πr²h
And the volume of the cone is 1/3(πr²h)

So the Volume of the cylinder is π(3r)²(2h) = 18πr²h
And the volume of the cone is 1/3π(4r)²(3h) = 48/3(πr²h) = 16πr²h
So the ratios of the volume of cylinder to cone be 18πr²h :16πr²h = 9 :8 (Ans)