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I need to compute the area of a $3D$ sphere centered on $0;0;0$ and the book I'm following says:

"If a curve $y = f (x)$ from $y = a$ to $y = b$ is revolved around the $x$ axis, the surface area of the resulting swept surface is"

enter image description here

What is this formula? I've never seen it before. I'd like to get a simple explanation on this or at least a simple proof why this should work

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Wiki page is very detailed – sabertooth Feb 25 '13 at 12:57
This might be what you're looking for. – Stefan Hansen Feb 25 '13 at 12:57
up vote 0 down vote accepted

It's proved on the wikipedia page for surface of revolution (not solid of revolution). That page also covers the specific case of a sphere.

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