Question

the surface area of a cylinder is 140π square millimeters. the cylinder is shown below. what is the height of the cylinder? millimeters submit

Explanation:

Step1: Write the formula for the surface area of a cylinder

The surface area formula of a cylinder is \(S = 2\pi r^{2}+2\pi rh\). Given \(S = 140\pi\) and \(r = 5\).

Step2: Substitute the values into the formula

Substitute \(S = 140\pi\) and \(r = 5\) into \(S = 2\pi r^{2}+2\pi rh\). We get \(140\pi=2\pi\times5^{2}+2\pi\times5h\).
Simplify \(2\pi\times5^{2}=2\pi\times25 = 50\pi\). So the equation becomes \(140\pi=50\pi + 10\pi h\).

Step3: Solve for \(h\)

Subtract \(50\pi\) from both sides: \(140\pi-50\pi=10\pi h\), which simplifies to \(90\pi=10\pi h\).
Divide both sides by \(10\pi\): \(h=\frac{90\pi}{10\pi}=9\).

Answer:

\(9\)