Question

what is the surface area of the cylinder with height 2 km and radius 5 km? round your answer to the nearest thousandth.

Explanation:

Step1: Recall total surface area formula

The total surface area \( S \) of a cylinder is \( S = 2\pi r^2 + 2\pi r h \), where \( r \) is radius, \( h \) is height.

Step2: Substitute given values

Substitute \( r = 5 \) km, \( h = 2 \) km:
\( S = 2\pi (5)^2 + 2\pi (5)(2) \)

Step3: Calculate each term

First term: \( 2\pi (25) = 50\pi \)
Second term: \( 2\pi (10) = 20\pi \)

Step4: Sum terms and compute value

Sum: \( 50\pi + 20\pi = 70\pi \)
Calculate numerical value: \( 70 \times 3.1415926535 \approx 219.91148575 \)

Step5: Round to nearest thousandth

Round \( 219.91148575 \) to 3 decimal places.

Answer:

219.911 square kilometers