\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
A sphere of radius \(r\) can be generated by revolving the semi-circle \(y=\sqrt{r^2-x^2}\) from \(x=-r\) to \(x=r\) around the x-axis.
Use the method of volumes of revolution to prove the formula for the volume of a sphere, \(V=\frac{4}{3}\pi r^3\).
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