Question

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

Explanation:

Step1: Calculate the area of the two bases

The formula for the area of a circle is \(A = \pi r^{2}\). For two bases, \(A_{bases}=2\pi r^{2}\). Given \(r = 4\) m and \(\pi=3.14\), we have \(A_{bases}=2\times3.14\times4^{2}=2\times3.14\times16 = 100.48\) \(m^{2}\).

Step2: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(A_{lateral}=2\pi r h\). Given \(r = 4\) m, \(h = 8\) m and \(\pi = 3.14\), we have \(A_{lateral}=2\times3.14\times4\times8=200.96\) \(m^{2}\).

Step3: Calculate the total surface area

The total surface area \(A = A_{bases}+A_{lateral}\). So \(A=100.48 + 200.96=301.44\) \(m^{2}\).

Answer:

\(301.44\space m^{2}\)