Question

find the surface area of a cylinder with a base diameter of 12 cm and a height of 7 cm. write your answer in terms of π, and be sure to include the correct unit.

Explanation:

Step1: Find the radius

The diameter \(d = 12\) cm. The radius \(r=\frac{d}{2}\), so \(r = \frac{12}{2}=6\) 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 \(r = 6\) cm and \(h = 7\) cm.
First, calculate \(2\pi r^{2}\): \(2\pi\times6^{2}=2\pi\times36 = 72\pi\).
Second, calculate \(2\pi rh\): \(2\pi\times6\times7=84\pi\).

Step4: Add the two parts together

\(S=72\pi + 84\pi=(72 + 84)\pi=156\pi\)

Answer:

\(156\pi\space cm^{2}\)