Question

what is the surface area of the cylinder with height 7 yd and radius 2 yd? round your answer to the nearest thousandth.

Explanation:

Step1: Recall the formula for the surface area of a cylinder

The formula for the surface area of a cylinder is \(S = 2\pi r^{2}+2\pi rh\), where \(r\) is the radius and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(r = 2\) yd and \(h=7\) yd.
First, calculate \(2\pi r^{2}\):
\(2\pi r^{2}=2\pi\times(2)^{2}=2\pi\times4 = 8\pi\)
Then, calculate \(2\pi rh\):
\(2\pi rh=2\pi\times2\times7=28\pi\)

Step3: Add the two parts together

\(S=8\pi + 28\pi=36\pi\)

Step4: Calculate the numerical value

Using \(\pi\approx3.1415926\), we have \(S = 36\times3.1415926=113.0973336\)

Answer:

\(113.097\)