I started out this lesson by getting the kids to think about infinity. This was crucial because I was going to use infinitely many polygonal pyramids to find the surface area of a sphere.
From the volume of pyramids: V = 1/3* B1 * h + 1/3 * B2 * h + ... + 1/3 * Bn * h
or V = h/3 * (B1 + B2 + ... + Bn)
Let n go to infinity and we can find the area of this and the sum of bases is the surface area. From this we come up with the formula for the surface area of a sphere. I just want the kids to know how to use the formula and to enjoy the presentation of the proof.
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