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,$\frac{112 \pi }{49 \pi } = h$
 
The π's cancel out and we are left with 
$h = \frac{112}{49}$ or 16/7 centimeters.

Hope this helped! :)