hi how can the following be proved using integral methods:

a) prove surface area of sphere, radius a, is $\displaystyle 4 \pi a^2$

b) prove area of a disk, radius a, is $\displaystyle \pi a^2$

c) prove volume of ball, radius a, is $\displaystyle \frac{4}{3} \pi a^3$

d) prove volume of axisymmetric cone of height h and base with radius a, is $\displaystyle \frac{1}{3}\pi a^2 h$

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i think my working of (a) is correct:

working of (a):|S| = $\displaystyle \int\int_{D} ||\frac{dr}{d\theta} X \frac{dr}{d\phi}|| dA$

use spherical co-ordinates:

$\displaystyle ||\frac{dr}{d\theta} X \frac{dr}{d\phi}|| = a^2sin \phi $

so:

|S| = $\displaystyle \int^{2\pi}_{0}\int^{\pi}_{0} a^2sin \phi d\phi d\theta$ = $\displaystyle \int^{2\pi}_{0} \left[ -a^2cos\phi \right]^{\pi}_0 d\theta$ = $\displaystyle \int^{2\pi}_{0} 2a^2 d\theta$ = $\displaystyle 4\pi a^2$

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how can i do the rest please. and what integration methods should I be using for each? thnx xxxx