Question

If the circumference of a great circle of a sphere is 22 pi, then its surface area is

Answer 1

A great circle is the intersection of a sphere and a plane passing through the sphere's center point. As such, we know the radius of a sphere's great circle is the same as the radius of the sphere itself.

We know the circumference of a circle is given by C = 2*pi*r, so if the great circle has C = 22*pi, r = (22*pi)/(2*pi) = 11

Thus, the radius of both the circle and sphere is 11. Since the surface area of a sphere is given by A = 4*pi*r^2, the surface area of this sphere will be 4*pi*(11)^2 = 4*pi*121 = 484*pi

Answer 2

thank you. I was checking my solution. and my steps match your steps. thanks