Question

find the surface area of a cylinder with a height of 6 in and a base radius of 4 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 lateral surface area

The formula for the lateral surface area of a cylinder is \(2\pi rh\).
Substitute \(r = 4\), \(h=6\), and \(\pi = 3.14\):
\(2\times3.14\times4\times6= 150.72\)

Step2: Calculate the area of the two bases

The formula for the area of a circle is \(\pi r^{2}\), and for two bases it is \(2\pi r^{2}\).
Substitute \(r = 4\) and \(\pi=3.14\):
\(2\times3.14\times4^{2}=2\times3.14\times16 = 100.48\)

Step3: Calculate the total surface area

The total surface area \(S\) of a cylinder is the sum of the lateral surface area and the area of the two bases, \(S=2\pi rh + 2\pi r^{2}\).
\(S=150.72+100.48\)

Answer:

\(251.2\) square inches