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## Main Question or Discussion Point

My brother thought of an alternative formula for the volume of a sphere:

(1/2)(∏R

could any one tell me why?

(1/2)(∏R

^{2})(2∏R).__it didn't work__could any one tell me why?

- Thread starter Sulfur
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- #1

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My brother thought of an alternative formula for the volume of a sphere:

(1/2)(∏R^{2})(2∏R).

__it didn't work__

could any one tell me why?

(1/2)(∏R

could any one tell me why?

- #2

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- #3

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the idea is that if a circle was turned around 180 degrees on a line through the middle of it, and if every frame of its rotation was kept there, it would make a sphere. The circumference is the distance the edge of the circle has to travel 360 degrees.

hmm.... maybe the problem is that different parts of the circle have to travel different lengths to go 360 degrees around.

Do you think if the problem was solved, I could derive another formula that is correct?

http://imageshack.us/a/img43/9046/circle1.png [Broken]

http://imageshack.us/a/img839/5682/circle2.png [Broken]

hmm.... maybe the problem is that different parts of the circle have to travel different lengths to go 360 degrees around.

Do you think if the problem was solved, I could derive another formula that is correct?

http://imageshack.us/a/img43/9046/circle1.png [Broken]

http://imageshack.us/a/img839/5682/circle2.png [Broken]

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- #5

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OK

could you give me an integral calculus tutorial?

could you give me an integral calculus tutorial?

- #6

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To get an idea and basic concepts, try Khan Academy. If you wan to learn the "standard" way, any university calc textbook will do. I'm not sure about online ones, but try Paul's Online Maths NotesOK

could you give me an integral calculus tutorial?

http://tutorial.math.lamar.edu/sitemap.aspx

PS Presuming you've learnt differentiation already.

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i haven't :(

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Then you should, so you can learn understanding instead of just memorising integrals.i haven't :(

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Note that if you slowly rotate a circle (in the manner of your pictures), the parts near the edge move farther than the parts near the middle. So every little rotation sweeps out volumes that are greater the farther away from the axis they are. For situations like that, you need calculus (or a smart Greek).

edit: I now noticed that you caught your mistake. well done.

edit: I now noticed that you caught your mistake. well done.

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