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

`(1)/(3)\pi r^(2) h`

The radius of the cone is given as 3 inches

Substituting in the formula we get

`(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.