Question

The cone shown has a volume of 12π in3. Find the volume of a cylinder with the same base and height as the cone.

A) 4π in3
B) 9π in3
C) 24π in3
D) 36π in3

Answer 1

The correct option is D.

Explanation:

The volume of cone is 12π in³.

The volume of cone is

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

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

Multiply both sides by 3.

`36\pi =\pi r^2h`

Divide both sides by π.

`36 =r^2h` ..... (1)

It is given that base and height of cone and cylinder are equal.

The volume of cylinder is

`V=\pi r^2h`

Using equation (1), we get

`V=\pi (36)`

`V=36\pi`

Therefore the volume of cylinder is 36π and option D is correct.