Question

the formula that represents the relationship between the volume, v, the radius, r, and the height, h, of a right cylinder is v = π(r)^2(h).
what is the height of a right cylinder that has a radius of 6 feet and a volume of 144π cubic feet?
enter your answer in the box.

feet

Explanation:

Step1: Substitute the given values into the formula

Given \(V = 144\pi\), \(r = 6\), substitute into \(V=\pi r^{2}h\). So \(144\pi=\pi\times(6)^{2}\times h\).

Step2: Simplify the equation

First, calculate \((6)^{2}=36\). The equation becomes \(144\pi = 36\pi h\).

Step3: Solve for \(h\)

Divide both sides of the equation \(144\pi = 36\pi h\) by \(36\pi\). \(\frac{144\pi}{36\pi}=h\). Since \(\frac{144}{36} = 4\) and \(\frac{\pi}{\pi}=1\), we get \(h = 4\).

Answer:

\(4\)