Question

a cylinder and a cone have the same volume. the cylinder has a radius of 2 inches and a height of 3 inches. the cone has a radius of 3 inches. what is the height of the cone?

Answer 1

2 inches
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Answer 2

The formula to find the volume of cylinder is

$\pi r^{2} h$

The radius of cylinder = 2 in

Height of the cylinder = 3 in

Substituting the values of r = 2 & h = 3

We get

Volume of cylinder

$\pi2^{2} (3)= 12\pi$

The formula to find the volume of cone is

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

The radius of the cone is given as 3 inches

Substituting in the formula we get

$\frac{1}{3} \pi 3^{2}h= 3\pi h$

But the volumes are given equal

So

$3\pi h= 12\pi$

Dividing by 3$\pi$ on both sides

we get

h = 4

The height of the cone is 4 inches.