Question

a cylinder has a diameter of 14 centimeters and a volume of 112pi cubic centimeters. what is the height, in centimeters, of the cylinder?

Answer 1

Formula for volume of a cylinder is

`v = \pi r^(2) h`

where r is the radius and h is the height

We can set v equal to 112π as we are given that.
We can set r to 7 as we are given the diameter, 14, and the radius is half of that.


`112 \pi= \pi 7^(2) h`

Simplify this equation,

`112 \pi = \pi *49*h`

Our goal is to to isolate h, as we are trying to find the height.
So divide 49π on both sides,
`(112 \pi )/(49 \pi ) = h`

The π's cancel out and we are left with

`h = (112)/(49)` or 16/7 centimeters.

Hope this helped! :)