I am sure this should have already be discussed somewhere in the past...(adsbygoogle = window.adsbygoogle || []).push({});

I have an intuitive problem with the area of a sphere. Following the mathematics of the metric and surfaces, I can easily derive the area of a sphere which is [itex]4 \pi R^{2} [/itex].

Now I'm have this problem:

Suppose I get a ring [circular] of radius R... then it's circumference is 2πR okay?

Then how could someone create a sphere? just roll it by an angle π around itself [check attachement]... But if I say so, won't the area be [itex] (2 \pi R) \times (\pi R) = 2 \pi^{2} R^{2} [/itex] ?

then one could say that each point on the circle is not going to cover a πR rotation, but a πr (r<R) ... double time because for each point which covers this rotation,there exists a symmetric one which covers the same... I think even with that, the area covered will be larger than the one given for a sphere.

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# Sphere surface area

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