A plane and a sphere intersect in a circle that has an area of 48pi. The distance between the plane and the center of the sphere is 3 units. Find the surface area of the sphere.

Question

I have very little knowledge n this level of geometry so a thorough explanation would be great!

Answer 1

There really isn't much geometry involved, but you must draw a sketch.

The sketch will have a circle with an off-center line through it

The problem really devolves to a circle (which is a representation of the sphere) with a line through it (which represents the plane)

The radius of the circle is is 1/2 the length of the line in your sketch.and

since the area of the circle is 48π, the radius is 24 units.

By the Pythagorean theorem the radius of the sphere is sqrt(576 + 9)

The area of the sphere is 4πr²