Question

consider a cylinder with a radius of 4 centimeters and a volume of 96π cubic centimete
find the height of the cylinder. be sure to use the correct unit in your answer.
4 cm
v = 96π cm³

Explanation:

Step1: Recall the volume formula for a cylinder

The volume formula for 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 are given that \(V = 96\pi\) \(cm^{3}\) and \(r = 4\) \(cm\). Substituting these into the formula gives \(96\pi=\pi\times(4)^{2}\times h\).

Step3: Simplify the equation

First, calculate \((4)^{2}=16\). So the equation becomes \(96\pi = 16\pi h\).

Step4: Solve for \(h\)

Divide both sides of the equation by \(16\pi\). \(\frac{96\pi}{16\pi}=h\). Since \(\frac{96}{16}=6\) and \(\frac{\pi}{\pi} = 1\) (for \(\pi
eq0\)), we get \(h = 6\).

Answer:

The height of the cylinder is \(6\) centimeters.