Question

The volume of a cylinder is 32.25 cubic inches. If a cone has the same height and radius as the cylinder, what is its volume?

Answer 1

The volume of a cylinder with a radius r and a height h:

$V_1=\pi r^2h$

The volume of a cone with a radius r and a height h:

$V_2=\dfrac{1}{3}\pi r^2h$

Therefore

$V_2=\dfrac{1}{3}V_1$

We have $V_1=32.25\ in^3$

Substitute:

$V_2=\dfrac{1}{3}\cdot32.25=10.75\ in^3$

Answer: The volume of a cone is equal 10.75 in³