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.
First, let's find the radius of the circle. We simply have
25π=π∗r225=r2r=5
Let's let R be the radius of the sphere.
R2=[52+r2]=[52+52]=50
Now, we can calculate the surface area of the sphere. We have
4πR2=4π∗50=200π
So, the answer is 200π
Thanks! :)