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.
The radius of the circle can be found as
25 pi = pi *r^2
25 = r^2
r = 5
Ler R be the radius of the sphere
R^2 = [ 5^2 + r^2 ] = [ 5^2 + 5^2 ] = 50
Surface area of sphere =
4 pi R^2 =
4 pi * 50 =
200 pi
+1475 
