13.3: 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.