Question

a cylinder has a diameter of 8 centimeters and a height of 16 centimeters. what is its surface area? 384π cm² 160π cm² 512π cm² 128π cm²

Explanation:

Step1: Calculate the radius

Given diameter \(d = 8\) cm, radius \(r=\frac{d}{2}=\frac{8}{2}=4\) cm.

Step2: Recall the surface - area formula for a cylinder

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

Step3: Substitute the values of \(r\) and \(h\) into the formula

We know \(r = 4\) cm and \(h=16\) cm.
First, calculate \(2\pi r^{2}\): \(2\pi\times(4)^{2}=2\pi\times16 = 32\pi\).
Second, calculate \(2\pi rh\): \(2\pi\times4\times16=128\pi\).

Step4: Find the total surface area

\(S=2\pi r^{2}+2\pi rh=32\pi + 128\pi=160\pi\) \(cm^{2}\).

Answer:

\(160\pi\ cm^{2}\)