Question

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

Answer 1

Answer:

The correct option is 3.

Step-by-step explanation:

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

The volume of a cone is

$V_1=\frac{1}{3}\pi r^2h$

Put V₁=12 in the value equation.

$12=\frac{1}{3}\pi r^2h$

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.

Answer 2

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