Question

find the surface area of a cylinder with a base radius of 2 yd and a height of 9 yd. 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, \(A_{bases}=2\pi r^{2}\). Substitute \(r = 2\) and \(\pi=3.14\):
\(A_{bases}=2\times3.14\times2^{2}=2\times3.14\times4 = 25.12\)

Step2: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(A_{lateral}=2\pi rh\). Substitute \(r = 2\), \(h = 9\) and \(\pi = 3.14\):
\(A_{lateral}=2\times3.14\times2\times9= 113.04\)

Step3: Calculate the total surface area

The total surface area \(A=A_{bases}+A_{lateral}\)
\(A=25.12 + 113.04=138.16\)

Answer:

\(138.16\space yd^{2}\)