Find the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?
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 × r3→eqn1
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