Question

Challenge: The distance around the middle of a sphere (the circumference) equals 37.699 in. What is the surface area of the sphere?

Answer 1

"The distance around the middle" means the circumference of the sphere, which is a circle.
use circumference of circle formula C = 2* pi* r = 37.699"

Now use surface are of sphere formula = 4* pi* r^2
this is the same as (2* pi* r) x (2* pi* r) / pi ..... yes ?!? :)
And we know that (2* pi* r) is C !!

So surface area of a sphere, if you KNOW the circumference = C* C / pi

So the area is = 37.699^2 / pi = 452.39 sq in