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?

Volume of a cylinder: [tex] \pi [/tex]r²h

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

[tex] \pi [/tex]r² = 25
Divide both sides by [tex] \pi [/tex].

r² = 7.96
Square root both sides.

r = 2.82 meters

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

2.82²h = 71.62
Divide by 2.82².

h = 9

The height of the cylinder is 9 square meters.