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

Answer:

h = 16x

Step-by-step explanation:

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

$V_s=V_c\\\\\dfrac{4}{3}\pi r^3=\dfrac{1}{3}\pi R^2h$

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

So,

$\dfrac{4}{3}\pi x^3=\dfrac{1}{3}\pi (\dfrac{x}{2})^2h\\\\4x^3=\dfrac{x^2}{4}h\\\\h=\dfrac{16x^3}{x^2}\\\\h=16x$

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