Question

A sphere and a cone have the same volume. The sphere has a radius x and height y. The cone has a radius of 1/2x. Find the height of the cone in terms of y.

Answer 1

h = 16x

Explanation:

The volume of a sphere and a cone is same such that,

`V_s=V_c\\\\(4)/(3)\pi r^3=(1)/(3)\pi R^2h`

We have, r = x, R = (1/2)x, h= ? (height of the cone)

So,

`(4)/(3)\pi x^3=(1)/(3)\pi ((x)/(2))^2h\\\\4x^3=(x^2)/(4)h\\\\h=(16x^3)/(x^2)\\\\h=16x`

So, the height of the cone is equal to 16x.