Question

A cone has a volume of 30 in ³.

What is the volume of a cylinder with the same radius
and height?

Answer 1

`90 \ in^(3)`

Explanation:

The volume of a cone is ¹/₃ the volume of the cylinder of a given radius and perpendicular height

`V_(C) = volume \ of \ cylinder \\\\ V_(c) = volume \ of \ cone\\\\ r = radius \\\\ h = perpendicular \ height`

`V_(C) = \pi r^(2)h \\\\ V_(c) = (1)/(3)\pi r^(2)h` →
`3V_(c) = \pi r^(2)h = V_(C)`

So if r and h are the same, then:

`V_(C) = 3V_(c)`

Therefore:

`V_(C) = 3(30) \\\\ V_(C) = 90`