Question

Suppose the volume of a right circular cylinder is 225 cubic meters and the area of its base is 25 square meters. What is the height of the cylinder?

Answer 1

Volume of a cylinder: $\pi$r²h

First we need to find the radius of the cylinder. It's area is 25. We can plug that into the area formula, $\pi$r² and solve for r (radius).

$\pi$r² = 25
Divide both sides by $\pi$.

r² = 7.96
Square root both sides.

r = 2.82 meters

Now plug the radius + volume into the volume formula and solve for h.
$\pi$2.82²h = 225
Divide by $\pi$.

2.82²h = 71.62
Divide by 2.82².

h = 9

The height of the cylinder is 9 square meters.

Answer 2

base area = 25 sq meters
area = PI*radius^2
radius = sq root [area / PI]
radius = sq root (25/PI)
base radius = 2.8209479177 meters
 
Cylinder Volume   =   π • r² • height
Therefore,
Cylinder height = Volume / [pi*radius^2]
Cylinder height = 225 / [PI*2.8209479177 ^ 2]
Cylinder height = 225 / [PI * 7.9577471544 ]
Cylinder height = 225 / 25
Cylinder height = 9 meters

Source:
Formulas
http://www.1728.org/diamform.htm
Calculator
http://www.1728.org/diam.htm