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)= (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
`(1)/(3)` to both of the sides of the equation.

`(1)/(3) 32.25= (1)/(3) \pi r^2h`

`10.75= (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.