Question

a cone and a cylinder have the same radii but the height of the cone is 3 times that of the cylinder.find the ratio of their volumes

Answer 1

Let radius of cylinder = r

Let radius of cone = R

Let height of cylinder = h

Let height of cone = H

Let volume of cylinder = v = πr²h

Let volume of cone = V = 1/3πr²h

Given that,

R = r

H = 3h

V/v = 1/3πR²H/ πr²h

V/v = 1/3πr²(3h) / πr²h (from q )

V/v = πr²h / πr²h

V/v = 1/1

V = v

So, volume of cylinder = volume of cone.

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