Question

consider a cylinder with a radius of 2 millimeters and a volume of 32π cubic millimeters. find the height of the cylinder. be sure to use the correct unit in your answer. the height of the cylinder is

Explanation:

Step1: Recall the formula for the volume of a cylinder

The volume formula of a cylinder is \( V=\pi r^{2}h\), where \(V\) is the volume, \(r\) is the radius, and \(h\) is the height.

Step2: Substitute the given values into the formula

We know that \(V = 32\pi\space mm^{3}\) and \(r = 2\space mm\). Substituting these into \(V=\pi r^{2}h\), we get \(32\pi=\pi\times(2)^{2}\times h\).

Step3: Simplify the equation

First, simplify \(\pi\times(2)^{2}\times h\) to \(4\pi h\). So the equation becomes \(32\pi = 4\pi h\).

Step4: Solve for \(h\)

Divide both sides of the equation \(32\pi = 4\pi h\) by \(4\pi\). \(\frac{32\pi}{4\pi}=h\). Since \(\frac{32\pi}{4\pi}=\frac{32}{4}\) (the \(\pi\) terms cancel out), \(h = 8\space mm\).

Answer:

\(8\space mm\)