Answer:
[tex]10000\pi[/tex]
Step-by-step explanation:
The formula for circumference is given by [tex]2\pi r[/tex]. Setting this equal to the circumference in the problem, we can find the radius of the sphere:
[tex]2\pi r=100\pi, \\r=\frac{100\pi}{2\pi},\\r=50[/tex]
Now we can use the formula for the surface area of a sphere:
Surface area of a sphere: [tex]A=4\pi r^2[/tex]
Using [tex]r=50[/tex]:
[tex]A=4\cdot \pi \cdot 50^2,\\A=4\cdot 2500\cdot \pi,\\A=\boxed{10000\pi}[/tex]
