Question

the lateral area of a cylinder is 286π square inches. the radius of the cylinders base is 16 inches. what is its height? inches

Explanation:

Step1: Recall the formula for lateral area of a cylinder

The lateral area formula of a cylinder is \(A = 2\pi rh\), where \(A\) is the lateral area, \(r\) is the radius, and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(A=280\pi\) and \(r = 16\). Substitute into \(A = 2\pi rh\): \(280\pi=2\pi\times16\times h\).

Step3: Solve for \(h\)

First, simplify the right - hand side: \(2\pi\times16\times h=32\pi h\). Then, divide both sides of the equation \(280\pi = 32\pi h\) by \(32\pi\). \(\frac{280\pi}{32\pi}=h\). Since \(\frac{\pi}{\pi}=1\), we have \(h=\frac{280}{32}=\frac{35}{4} = 8.75\).

Answer:

\(8.75\)