Question

find the surface area of a cylinder with a height of 9 m and a base radius of 6 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 circular bases

The formula for the area of a circle is \(A = \pi r^{2}\). Given \(r = 6m\) and \(\pi=3.14\), the area of one - base is \(A_{base}=\pi r^{2}=3.14\times6^{2}=3.14\times36 = 113.04m^{2}\). The area of two bases is \(A_{two - bases}=2\times113.04 = 226.08m^{2}\).

Step2: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(A_{lateral}=2\pi rh\). Given \(r = 6m\), \(h = 9m\), and \(\pi = 3.14\), we have \(A_{lateral}=2\times3.14\times6\times9=3.14\times108 = 339.12m^{2}\).

Step3: Calculate the total surface area

The formula for the total surface area of a cylinder is \(A=A_{two - bases}+A_{lateral}\). Substitute the values from Step 1 and Step 2: \(A=226.08 + 339.12=565.2m^{2}\).

Answer:

\(565.2m^{2}\)