I was just thinking about how you would calculate the volume of a sphere last night, and tried it thusly, using the logic that a sphere is nothing but a bunch of infinitesimally thin circles with increasing radius from 0 to r, and then from decreasing radius r to 0:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int^{R}_{0} \pi r^{2}dr= \frac{1}{3} \pi R^{3}[/tex]

This, I thought should be one hemisphere, so I multiplied the result by 2, getting [tex]\frac{2}{3} \pi R^{3}[/tex]. This, of course, is not the volume of a sphere. Why did my method not work?

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# Volume of a sphere

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