+1694 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.
+1790 First, let's find the radius of the circle. We simply have
\(25 \pi = \pi *r^2 \\ 25 = r^2 \\r = 5 \)
Let's let R be the radius of the sphere.
\(R^2 = [ 5^2 + r^2 ] = [ 5^2 + 5^2 ] = 50 \)
Now, we can calculate the surface area of the sphere. We have
\(4 \pi R^2 = \\ 4 \pi * 50 = \\ 200 \pi\)
So, the answer is \(200 \pi \)
Thanks! :)
