anonymous
  • anonymous
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.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
I assume TT is supposed to be \(\pi\). How did you want to set this up?
anonymous
  • anonymous
correct I didn't know how to make the pi symbol.
anonymous
  • anonymous
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 \[\pi (2r^3/3 - (-2r^3/3)) = 4\pi r^2/3\]

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anonymous
  • anonymous
yay, another student given the answer with no effort or thinking required. GJ!
anonymous
  • anonymous
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
  • anonymous
If you want to actually understand what's going on you should probably elaborate more on what part is confusing you, etc.

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