Quote:
Originally posted by Jared
Here is the complete proof, I added the previous proof of the 4/3 figure into it......
Now for connecting the dots ...
(The following are lines; they are represented with the omitted -- on top).
CE = AF = AB
CA = CD, so CA^2 = CD^2
CA^2 + CB^2 = AB^2, and we see above that AB = CE, so AB^2 = CE^2
So therefore, since CA^2 = CD^2
CD^2 + CB^2 = CE^2
So now a proportion is clearly established.
Circle (cone) + circle (sphere) = circle (cylinder), so,
Circle (sphere) = circle (cylinder) - circle (cone).
The Volume of Cylinder (pi * r^3) - Volume of Cone (1/3 * pi * r^3) = 2/3 * pi * r^3, so,
Multiplying by 2 (for two hemispheres) gives 4/3 * pi * r^3.
:p
You lost me again. :confused: