A plane and a sphere intersect in a circle. The circle has an area of $25 \pi$. The distance between the plane and the center of the sphere is $5$ units. Find the surface area of the sphere.

Suppose the radius of the circle = r units

\(\pi r^2 = 25\pi\\ r = 5\)

Then, the radius of the sphere is \(\sqrt{r^2 + 5^2} = 5 \sqrt 2\) units.

Then the surface area is \(4 \pi (5 \sqrt 2)^2 = 200\pi\).