# Volume of a sphere

Discussion in 'Math' started by mentaaal, Feb 11, 2009.

1. ### mentaaal Thread Starter Senior Member

Oct 17, 2005
451
0
Hey guys, I have a question relating to integration which is puzzling me.

I figured that I would try and derive the volume of a sphere myself. Having never done this before I started out with a strategy that to me seems perfectly logical. If it can be seen from the 10 second scribble in paint, I imagine the circle i've drawn to be a 3-d sphere. If i cut the sphere up in cross-sectional slices with cross sectional area πr^2 and integrate from 0 to r, taking the zero point to be the left most point on the circle, I would have found the volume of a hemisphere. Therefore I would need to multiply this integral by two to get the total volume.

Like this: 2∫πr^2 dr (from 0 to r) = [2πr^3]/3

Obviously this is wrong so could someone point out the flaw in my approach as I am off by a factor of 2.

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Last edited: Feb 11, 2009
2. ### Alexei Smirnov Active Member

Jan 7, 2009
43
1
When you integrate from 0 to r, the radius of the circle is not equal r,
it is equal to sqrt(1-r^2), so you have to take
2*∫π(1-r^2)dr = 2πr^3(1-1/3) = 4πr^3/3.

3. ### mentaaal Thread Starter Senior Member

Oct 17, 2005
451
0
Yes I can see now how I was wrong. Thank you very much!

4. ### nene biggie New Member

Feb 28, 2009
3
0
volume ofsphere formular =4/3pie r because it has four quaters according to my view.

5. ### Mark44 Well-Known Member

Nov 26, 2007
626
1
We've already established in this thread that the volume of a sphere is 4/3 * πr$^{3}$. This formula has been known for hundreds of years.