Question

what is the surface area of the cylinder with height 2 km and radius 7 km? 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 \(S = 2\pi r(r + h)\), where \(r\) is the radius and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(r = 7\) km and \(h = 2\) km. Substitute into the formula:
\(S=2\pi\times7\times(7 + 2)\)
First, calculate \(7+2 = 9\). Then \(S = 2\pi\times7\times9\).
Since \(2\times7\times9=126\), the formula becomes \(S = 126\pi\).

Step3: Calculate the numerical value

Using \(\pi\approx3.14159265\), then \(S=126\times3.14159265\).
\(126\times3.14159265 = 395.8406739\)

Answer:

\(395.841\)