Volume of Spheres with Deduction
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) Check the cross-sections (circle and annulus) have the same area
(c) Using that the volume of the cone is 1/3 of the volume of the cylinder, show that the volume of the sphere of radius r is 4/3 π r³.