Question

what is the surface area of the cylinder with height 7 in and radius 7 in? 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 \(r = 7\) in and \(h=7\) in.
First, calculate \(2\pi r^{2}\):
\(2\pi r^{2}=2\pi\times(7)^{2}=2\pi\times49 = 98\pi\)
Then, calculate \(2\pi rh\):
\(2\pi rh=2\pi\times7\times7 = 98\pi\)

Step3: Add the two parts together

\(S=98\pi + 98\pi=196\pi\)

Step4: Calculate the numerical value

Using \(\pi\approx3.14159265\), we have \(S = 196\times3.14159265\)
\(S=196\times3.14159265=615.7521594\)

Answer:

\(615.752\)