Question

find the surface area of a cylinder with a height of 5 yd and a base radius of 2 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 lateral surface area

The formula for the lateral surface area of a cylinder is \(2\pi rh\).
Substitute \(r = 2\), \(h = 5\), and \(\pi=3.14\):
\(2\times3.14\times2\times5=62.8\)

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 \(r = 2\) and \(\pi = 3.14\):
\(2\times3.14\times2^{2}=2\times3.14\times4 = 25.12\)

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.
\(S=62.8 + 25.12=87.92\)

Answer:

\(87.92\ \text{yd}^{2}\)