Question

If the volume of a cylinder is 72 inches^3, what is the volume of a cone that fits exactly inside the cylinder

Answer 1

Hello!

The answer is:

$ConeVolume=24in^{3}$

Why?

Since we know the volume of the cylinder,  and we also know that both cylinder and cone have the same height and same base diameter, we can calculate the volume of a cone that fits exactly inside the cylinder using the following relation:

$CylinderVolume=3ConeVolume\\\\ConeVolume=\frac{CylinderVolume}{3}$

So, from the statement we know that the volume of the cylinder is  $72in^{3}$

Then, substituting it into the formula, we have:

$ConeVolume=\frac{72in^{3} }{3}=24in^{3}$

Have a nice day!

Answer 2

The formula for volume of a cylinder is V = PI x r^2 x h

The formula for the volume of a come is V = PI x r^2 x h/3

Divide the area of the cylinder by 3:

72/3 = 24

The volume of the cone is 24 cubic inches.