The volume of a solid sphere of radius r is given by the equation V=4/3TTr^3. Derive this equation by using either the disk or shell method for finding the volume of a solid of revolution.

Question

The volume of a solid sphere of radius r is given by the equation V=4/3TTr^3.  Derive this equation by using either the disk or shell method for finding the volume of a solid of revolution.

anonymous · Answer

I assume TT is supposed to be $\pi$. 

How did you want to set this up?

anonymous · Answer

correct I didn't know how to make the pi symbol.

anonymous · Answer

Using Disk method:
$$\pi \int\limits_{-r}^{r} (r^2 - x^2)^2dx = \int\limits_{-r}^{r} (r^2-x^2)$$
$$= r^2x-x^3/3$$ from -r to r
$$\pi (2r^3/3 - (-2r^3/3)) = 4\pi r^2/3$$

anonymous · Answer

yay, another student given the answer with no effort or thinking required. GJ!

anonymous · Answer

Btw, if you just want answers you can probably google it faster than we can type it for you.. see: http://en.wikipedia.org/wiki/Sphere#Volume_of_a_sphere

anonymous · Answer

If you want to actually understand what's going on you should probably elaborate more on what part is confusing you, etc.