Question

find the surface area of a cylinder with a height of 5 ft and a base radius of 3 ft. 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 \(A = \pi r^{2}\). For two bases, \(A_{bases}=2\pi r^{2}\). Substitute \(r = 3\) and \(\pi=3.14\):
\(A_{bases}=2\times3.14\times3^{2}=2\times3.14\times9 = 56.52\)

Step2: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(A_{lateral}=2\pi rh\). Substitute \(r = 3\), \(h = 5\) and \(\pi = 3.14\):
\(A_{lateral}=2\times3.14\times3\times5=94.2\)

Step3: Calculate the total surface area

The total surface area \(A = A_{bases}+A_{lateral}\)
\(A=56.52 + 94.2=150.72\)

Answer:

\(150.72\space ft^{2}\)