Question

find the surface area of a cylinder with a base diameter of 6 m and a height of 4 m. write your answer in terms of π, and be sure to include the correct unit.

Explanation:

Step1: Find the radius

The diameter \(d = 6m\), so the radius \(r=\frac{d}{2}=\frac{6}{2}=3m\).

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 \(r = 3m\) and \(h = 4m\).
First, calculate \(2\pi r^{2}\): \(2\pi\times(3)^{2}=2\pi\times9 = 18\pi\).
Second, calculate \(2\pi rh\): \(2\pi\times3\times4=24\pi\).

Step4: Sum the two parts

\(S=18\pi + 24\pi=(18 + 24)\pi=42\pi\)

Answer:

\(42\pi m^{2}\)