關於球體的表面面積&體積.................

有種用integration既方法冇咁深，但應該唔係formal proof。
Let the equation be x^2+y^2=r^2. Then the volume of the sphere will be generated by revolving the equation about the y-axis.
http://hk.geocities.com/cowcow138168/sphere.jpg
Use S to denote the integral sign.
Upper limit be r and lower limit be -r.
Volume
=S(pi)x^2dy
=S(pi)(r^2 - y^2)dy
=(r^2y - y^3/3)(pi)
=(r^2(r)-(r)^3/3)-(r^2(-r)-(-r)^3/3)(pi)
=(r^3-r^3/3)-(-r^3+r^3/3)(pi)
=(2r^3-2r^3/3)(pi)
=4/3(pi)r^3
Let V be the volume of the sphere
V=4/3(pi)r^3
Differentiate both sides with respect to r
dV/dr=4/3(3)(pi)r^2
dV/dr=4(pi)r^2
A=4(pi)r^2

要明就要識integration, 由於好難打出嚟, 所以請參考:

http://mathworld.wolfram.com/Sphere.html