Surface Area of a Sphere The area of a disk enclosed by a circle - TopicsExpress

Surface Area of a Sphere The area of a disk enclosed by a circle of radius R is Pi*R2. The formula for the circumference of a circle of radius R is 2*Pi*R. A simple calculus check reveals that the latter is the derivative of the former with respect to R. Similarly, the volume of a ball enclosed by a sphere of radius R is (4/3)*Pi*R3. And the formula for the surface area of a sphere of radius R is 4*Pi*R2. And, you can check that the latter is the derivative of the former with respect to R. Coincidence, or is there a reason?

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