Question

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

Answer 1

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

Then their radius will be r

and height of cylinder and cone will be 2r

Hence required ratio = Volume of sphere : Volume of cylinder : Volume of cone

$\frac{4}{3}$$\pi$$r^3$ : $\pi$$r^2$h : $\frac{1}{3}$ $\pi$$r^2$h

4$\pi$$r^3$ : 3$\pi$$r^2$h : $\pi$$r^2$h [ h = 2r]

4$\pi$$r^3$ : 3$\pi$$r^2$2r : $\pi$$r^2$2r

4$r^3$: 6$r^3$ : 2$r^3$

2:3:1