Question

A cone has a volume of 12 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?

6 in3
24 in3
36 in3
48 in3

Answer 1

36in^3
as the volume of a cone is 1/3 that of the volume of a cylinder the smallest cylinder that the cone can fit inside of is one that is exactly 3x its the volume

Answer 2

The correct option is 3.

Explanation:

It is given that the volume of a cone is 12 cubic inches.

The volume of a cone is

`V_1=(1)/(3)\pi r^2h`

Put V₁=12 in the value equation.

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

Multiply both sides by 3.

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

Where, r is radius of base, h is height.

It is given that the cone fits exactly inside of the cylinder. It means the height and the radius of the cylinder is same.

The volume of a cylinder is

`V_2=\pi r^2h`

Using equation (1) we get

`V_2=36`

The volume of cylinder is 36 cubic inches. Therefore the correct option is 3.