c.s.a of a hemisphere

Question

Here is a question which I would like to understand. I want to know

How to prove that c.s.a of a hemisphere is $2\pi r^2$ ? enter image description here

I'm a 10th CLASS average student,so please keep it simple.

Thank you....

Thanks. How is that different from just plain old surface area? — Gerry Myerson, Feb 23 '14 at 10:43
@GerryMyerson it does not include the plane surface area $\pi r^2$ — happymath, Feb 23 '14 at 10:54
OK. There is no fully rigorous way to get that formula without using Calculus (or at any rate, some limit calculation). Have a look at http://en.wikipedia.org/wiki/Sphere#Area to see what you're up against. You might enjoy http://www.youtube.com/watch?v=5RrjbeuoNOA which is a video showing how Archimedes did it. — Gerry Myerson, Feb 23 '14 at 10:57
See also http://math.stackexchange.com/questions/106865/how-did-archimedes-find-the-surface-area-of-a-sphere --- in fact, type Archimedes area of a sphere into Google and lots of pages come up. — Gerry Myerson, Feb 23 '14 at 11:00

score 0 · Accepted Answer · answered Feb 23 '14 at 09:46

0

We know that C.S.A of a sphere is $4\pi r^2$. Therefore C.S.A of hemisphere is $2\pi r^2$.

answered Feb 23 '14 at 09:46

happymath

How is csa of a sphere $4\pi r^2$, i need a proff. – Feb 23 '14 at 10:58
@ShivamGautam are u comfortable with integration – happymath Feb 23 '14 at 11:00
this might help mathcentral.uregina.ca/qq/database/QQ.09.99/wilkie1.html – happymath Feb 23 '14 at 11:06

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