Answer:
<em>The surface area of the sphere is 314 mi².</em>
Step-by-step explanation:
According to the given diagram, the diameter of the sphere is 10 mi.
If the radius is
, then diameter ![=2r](https://tex.z-dn.net/?f=%3D2r)
So....
![2r=10\\ \\ r=\frac{10}{2}= 5](https://tex.z-dn.net/?f=2r%3D10%5C%5C%20%5C%5C%20r%3D%5Cfrac%7B10%7D%7B2%7D%3D%205)
<u>Formula for the surface area of a sphere</u>: ![A_{S}= 4\pi r^2](https://tex.z-dn.net/?f=A_%7BS%7D%3D%204%5Cpi%20r%5E2)
Plugging the value of
into this formula, we will get...
![A_{S}=4\pi(5)^2\\ \\ A_{S}=4\pi(25)\\ \\ A_{S}=4(3.14)(25)\ \ [Using\ \pi=3.14]\\ \\ A_{S}=314](https://tex.z-dn.net/?f=A_%7BS%7D%3D4%5Cpi%285%29%5E2%5C%5C%20%5C%5C%20A_%7BS%7D%3D4%5Cpi%2825%29%5C%5C%20%5C%5C%20A_%7BS%7D%3D4%283.14%29%2825%29%5C%20%5C%20%5BUsing%5C%20%5Cpi%3D3.14%5D%5C%5C%20%5C%5C%20A_%7BS%7D%3D314)
So, the surface area of the sphere is 314 mi².