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Volume of Spheres with Proof

The figure shows a hemisphere of radius r and a cylinder of base radius and height r with an inverted cone of the same height and base radius removed. Drag the red point to see the cross-sections of the two solids at a height h. (a) Express x and y in terms of r and h. (b) Are the cross-sections equal in area? (c) Hence show that the volume of the sphere of radius r is 4/3 π r³.