I'm trying to prove the volume of a sphere is (4/3)(pi)r^3. (Sorry I haven't figured out the tex thing yet)(adsbygoogle = window.adsbygoogle || []).push({});

I was thinking that the volume of a sphere is the sum of the circular cross-sections that make it up. Since "r" is different for each cross-section, you put in the variable "x" and get:

(pi)x^2.

The height of the sphere can be represented by the change in y, (dy) so now we get the integral:

int{ (pi)x^2*dy }

Since we need the variable of integration in terms of y, I went to the equation of a circle.

x^2 + y^2 = r^2

So, x^2 = r^2 - y^2

Substituting that into the integral we get the final intergral:

int { (pi)(r^2-y^2)*dy }

This is as far as I can think this out. Where did I make a mistake or where do I need to go from here?

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Jameson

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# Proof of Volume of a Sphere

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