Question

find the surface area of the cylinder. sa =? π ft² leave your answer in terms of π

Explanation:

Step1: Calculate the area of the two circular bases

The formula for the area of a circle is \(A = \pi r^{2}\). Given \(r = 4\) ft, the area of one base is \(\pi\times4^{2}=16\pi\) \(ft^{2}\). For two bases, it is \(2\times16\pi = 32\pi\) \(ft^{2}\).

Step2: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(A = 2\pi r h\). Here \(r = 4\) ft and \(h = 12\) ft. So, \(2\pi\times4\times12=96\pi\) \(ft^{2}\).

Step3: Calculate the total surface area

The total surface area \(SA\) of a cylinder is the sum of the areas of the two bases and the lateral surface area. So, \(SA=32\pi + 96\pi\).

Answer:

\(128\pi\) \(ft^{2}\)