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

Volume of a cone = 1/3 r² π h
Volume of a cylinder = r² π h = 3 · V ( cone ) = 3 · 12 = 36 in³

Answer 2

Answer:

$\text{Volume of cylinder}=36\text{ in}^3$

Step-by-step explanation:

We have been given that a cone has a volume of 12 cubic inches. We are asked to find the volume of a cylinder that the cone fits exactly inside of.

Since the cone exactly fits inside the cone, so the radius of cylinder will be equal to radius of cone.

We also know that volume of cone that fits exactly inside a cylinder is 1/3 of the volume of the cylinder. So the volume of of cylinder will be three times the volume of cone.

$\text{Volume of cylinder}=\pi r^2h$

$\text{Volume of cone}=\frac{\pi r^2h}{3}$

$\text{Volume of cylinder}=3\times 12\text{ in}^3$

$\text{Volume of cylinder}=36\text{ in}^3$

Therefore, the volume of the cylinder will be 36 cubic inches.