Question

find the surface area of a cylinder with a height of 8 ft and a base diameter of 4 ft. use the value 3.14 for π, and do not do any rounding. be sure to include the correct unit.

Explanation:

Step1: Find the radius

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

Step2: Calculate the surface area formula

The surface area formula of a cylinder is \(S = 2\pi r^{2}+2\pi rh\).
Substitute \(r = 2\), \(h = 8\) and \(\pi=3.14\) into the formula.
First term: \(2\pi r^{2}=2\times3.14\times2^{2}=2\times3.14\times4 = 25.12\)
Second term: \(2\pi rh=2\times3.14\times2\times8=100.48\)

Step3: Sum up the two terms

\(S=25.12 + 100.48=125.6\)

Answer:

\(125.6\mathrm{ft}^{2}\)