Q. 24 4.3( 3 Votes )

Find the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?

Answer :

Let the radius of cylinder, cone and sphere be ‘r’ cm

Let the diameter of cylinder, sphere and cone be ‘2r’ units

Height of cylinder, cone, sphere = h = 2r units

Volume of cylinder = π(r2)h

Volume of cylinder = π × r2 × 2r (putting value of h)

Volume of cylinder = 2π × r3eqn1

Volume of sphere

Volume of cone(put the value of h)

Volume of cone

Volume of cone

Ratio of volume of cylinder to that of a cone to that of a sphere as:

Volume of cylinder : Volume of Cone : Volume of sphere

(dividing the above relation by (πr3)

(dividing the above ratio by 2)

3 : 1 : 2 (multiplying the above ratio by 3)

Ratio of volume of cylinder to that of cone to that of sphere is 3 : 1 : 2

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