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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?

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