Notice that if you drag the slider, the volume of half a sphere (hemisphere) is equal to the volume of the cylinder minus the volume of the cone. So, half a sphere = [math]\pi[/math]r[sup]2[/sup]h - [math]\frac{1}{3}\pi[/math]r[sup]2 [/sup]h. Therefore, half a sphere = [math]\frac{2}{3}\pi[/math]r[sup]2[/sup]h. If half a sphere = [math]\frac{2}{3}\pi[/math]r[sup]2[/sup]h, then an entire sphere equals [math]\frac{4}{3}\pi[/math]r[sup]2 [/sup]h. And, a sphere's radius and height are equal, so the formula can be cleaned up to [math]\frac{4}{3}\pi[/math]r[sup]3[/sup]