Question

what is the surface area of the cylinder with height 7 yd and radius 8 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 \(r = 8\) yd and \(h=7\) yd.
First, calculate \(2\pi r^{2}\):
\(2\pi r^{2}=2\pi\times8^{2}=2\pi\times64 = 128\pi\)
Then, calculate \(2\pi rh\):
\(2\pi rh=2\pi\times8\times7=112\pi\)

Step3: Add the two parts together

\(S=128\pi + 112\pi=(128 + 112)\pi=240\pi\)

Step4: Calculate the numerical value

Using \(\pi\approx3.14159265\), we have \(S = 240\times3.14159265=754.011036\)

Answer:

\(754.011\)