Surface Area
The surface area of a sphere is related to the area of a circle. How many great circles do you need to cover the entire surface area of a sphere? (A great circle is the circle with a center that is the same as the sphere's center.) You might want to use an orange to help explore this problem.
Devise a formula which relates the surface area of sphere with the area of a great circle of the sphere.
What happens to the area of a circle when you double the diameter of a circle? Why does this happen? What happens to the area if you triple the diameter? Explain. What happens to the surface area of a sphere if you double the diameter? If you triple the diameter?
Submit your idea for an investigation to InterMath.
