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Q: Why is the area of a circle equal to πR2?

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Oranges:Imagine taking an orange wedge and opening it so that the triangles all point “up” instead of towards the same point. As the number of triangles “approaches infinity” the circle can be taken apart and rearranged to fit almost perfectly into an “R by πR” box with an area of πR2. Calculus:On the mathier side of things, the circumference is the differential of the area. That is; if you increase the radius by “dr”, which is a tiny, tiny bit, then the area increases by Cdr where C is the circumference. A mathematician will forget the equation for the area of a circle (A=πR2), but remember that the circumference is its differential.