Question

a right circular cylinder has a height of 16 inches and a volume of 5,184π cubic inches. what is the radius, in inches, of this cylinder?

Explanation:

Step1: Write the formula for the volume of a cylinder

The volume formula of a right - circular 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

Given \(V = 5184\pi\) and \(h=16\). Substitute into \(V=\pi r^{2}h\), we get \(5184\pi=\pi r^{2}\times16\).

Step3: Solve for \(r^{2}\)

Divide both sides of the equation \(5184\pi=\pi r^{2}\times16\) by \(16\pi\).
\(\frac{5184\pi}{16\pi}=r^{2}\), since \(\frac{5184}{16}=324\), so \(r^{2} = 324\).

Step4: Solve for \(r\)

Take the square root of both sides. \(r=\sqrt{324}\), and \(r = 18\) (we take the positive value since \(r\) represents a length).

Answer:

\(18\)