Question

find the surface area of a cylinder with a base radius of 2 in and a height of 3 in.
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 \(r = 2\) in and \(\pi=3.14\), we have \(A_{bases}=2\times3.14\times2^{2}=2\times3.14\times4 = 25.12\) in².

Step2: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(A_{lateral}=2\pi rh\). Given \(r = 2\) in, \(h = 3\) in and \(\pi = 3.14\), we have \(A_{lateral}=2\times3.14\times2\times3=37.68\) in².

Step3: Calculate the total surface area

The total surface area \(A=A_{bases}+A_{lateral}\). So \(A = 25.12+37.68=62.8\) in².

Answer:

\(62.8\) in²