Answer:
351.9 mi^2
Step-by-step explanation:
The surface area of a cylinder can be found using the following formula.
[tex]SA=2\pi r^2+2\pi rh[/tex]
We know that the height of the cylinder is 10 miles and the radius is 4 miles.
h= 10 mi
r= 4 mi
[tex]SA=2\pi (4 mi)^2+2\pi (4 mi)(10 mi)[/tex]
First, evaluate the exponent 4 mi^2.
4 mi^2= 4 mi * 4 mi = 16 mi^2
[tex]SA=2\pi 16 mi^2+2\pi (4 mi)(10 mi)[/tex]
Next, multiply 16 and 2pi
[tex]SA=100.530965 mi^2+2\pi(4 mi)(10mi)[/tex]
Next, multiply 4 and 10
[tex]SA=100.530965 mi^2+2\pi40mi^2[/tex]
Multiply 40 and 2 pi
[tex]SA=100.530965 mi^2+251.327412mi^2[/tex]
Add the 2 numbers together
[tex]SA=351.858377 mi^2[/tex]
Round to the nearest tenth. The 5 in the hundredth place tells us to round the 8 to a 9 in the tenth place.
[tex]SA=351.9 mi^2[/tex]
The surface area of the cylinder is about 351.9 square miles.
