Thread: Surface area of a sphere View Single Post
 P: 126 1. The problem statement, all variables and given/known data Calculate the area for 3D sphere. 2. Relevant equations I know there's this formula for surface of revolution: $$A=2\pi\int_{a}^{b}f(x)\sqrt{1+ f'(x)^2}\:\mathrm{d}x$$ 3. The attempt at a solution I thought of dividing the the sphere into slices, each of which contains a ring. The length of each ring is $2\cdot\pi\cdot r$, with $r=\sqrt{R^2-x^2}$. We could then integrate: $$\int_{-R}^{R}2\pi\sqrt{R^2-x^2}\:\mathrm{d}x=4\pi\int_{0}^{R}\sqrt{R^2-x^2}\:\mathrm{d}x=\pi R^2$$ But this is not correct so there must be something wrong... PS: Just out of curiosity, is there any way to prove the formula for the surface are of an n-sphere using calculus? (the one with Γ)