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

Question

asked Sep 13, 2020 143k views

1 Answer

Brana · Answer 1 · 2020-09-16T15:28:43+0000

The volume of a cylinder is given by

$V=\pi hr^2$

Whereas the volume of a cone is given by

$V=(1)/(3)\pi hr^2$

Since the cylinder has radius x and height y, its volume is

$V = \pi x^2y$

And since the cone has a radius 2x, its volume is

$V = \pi (2x)^2 h = 4\pi x^2h$

where h is the height of the cone.

We know that the two volumes are the same, so we can build the equation and solve it for h:

$\pi x^2y = 4\pi x^2h$

Simplify
$\pi x^2$ from both sides:

y = 4h

Divide both sides by 4:

h = (y)/(4)