(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Why is this method not valid-moments?

I'm trying to find the moment of inertia for asolid sphere, I've seen and understand the correct method, but I can't see anything wrong with this method, except the answer.

[tex]I=\int r^2 dm[/tex]

[tex]m=\delta V=\frac{4}{3}\delta\pi r^3[/tex]

[tex]dm=4\delta\pi r^2 dr[/tex]

Thus,

[tex]I=4\delta\pi\int r^4dr[/tex]

Which after some work, turns out to be, incorrectly,

[tex]I=\frac{3}{5}r^2m[/tex].

The correct answer is,

[tex]I=\frac{2}{5}r^2m[/tex].

Thanks in advance.

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# Why is this method not valid-moments?

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