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

This math question is under the Solid Mensuration topic. Let us recap the formulas of the volume of both the cylinder and the cone.
$V_{cylinder}= \pi r^2h$
$V_{cone}= \frac{1}{3} \pi r^{2}h$

So if the volume of the cylinder is 32.25 inches,
$32.25=V_{cylinder}$
Then,
$32.25= \pi r^2h$

So, to obtain the value of the volume of the cone is we simply multiply $\frac{1}{3}$ to both of the sides of the equation.
$\frac{1}{3} 32.25= \frac{1}{3} \pi r^2h$
$10.75= \frac{1}{3} \pi r^2h$
$10.75=V_{cone}$ [/tex]
So its value if the radius and its height is the same as to the cylinder is 10.75 cubic inches.