Question

find the surface area of a cylinder with a base radius of 2 cm and a height of 3 cm. write your answer in terms of π, and 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 \(A = \pi r^{2}\). For two bases, \(A_{bases}=2\pi r^{2}\). Given \(r = 2\space cm\), then \(A_{bases}=2\pi\times(2)^{2}=8\pi\space cm^{2}\)

Step2: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(A_{lateral}=2\pi r h\). Given \(r = 2\space cm\) and \(h = 3\space cm\), then \(A_{lateral}=2\pi\times2\times3 = 12\pi\space cm^{2}\)

Step3: Calculate the total surface area

The total surface area \(A = A_{bases}+A_{lateral}\). So \(A=8\pi + 12\pi=20\pi\space cm^{2}\)

Answer:

\(20\pi\space cm^{2}\)