Question

the volume of a cylinder is 2,200π cubic inches. the diameter of the circular base is 10 inches. what is the height of the cylinder? recall the formula ( v=pi r^{2}h ).

Explanation:

Step1: Find the radius

Since the diameter \(d = 10\) inches, and \(r=\frac{d}{2}\), then \(r = 5\) inches.

Step2: Substitute into the volume formula

Given \(V=\pi r^{2}h\) and \(V = 2200\pi\), substitute \(r = 5\) into the formula:
\(2200\pi=\pi\times(5)^{2}\times h\)
Simplify the equation:
\(2200\pi=\pi\times25\times h\)
Divide both sides by \(25\pi\):
\(h=\frac{2200\pi}{25\pi}\)
Cancel out \(\pi\):
\(h=\frac{2200}{25}=88\)

Answer:

\(88\) inches