Question

the lateral area of a cylinder is 112π square feet. the diameter of the cylinder is 13 feet. what is its height? round your answer to the nearest hundredth. feet

Explanation:

Step1: Recall the formula for lateral area of a cylinder

The lateral area formula of a cylinder is \(A = 2\pi rh\) (where \(r\) is the radius and \(h\) is the height). Given \(d = 13\) feet, so \(r=\frac{d}{2}=\frac{13}{2}=6.5\) feet. And \(A = 112\pi\).

Step2: Substitute values into the formula

Substitute \(A = 112\pi\) and \(r = 6.5\) into \(A=2\pi rh\). We get \(112\pi=2\pi\times6.5\times h\).

Step3: Solve for \(h\)

First, divide both sides of the equation \(112\pi=2\pi\times6.5\times h\) by \(2\pi\).
\(\frac{112\pi}{2\pi}=\frac{2\pi\times6.5\times h}{2\pi}\).
Simplify: \(56 = 6.5h\).
Then \(h=\frac{56}{6.5}\approx8.62\).

Answer:

\(8.62\)