G.GGMD.3 Volume of Spheres

Sphere, Volume
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) Using the formulas of each, create a formula of the figure on the right (hint: volume of a cylinder minus the volume of a cone). (c) Multiply your answer in part b by 2 because the figure on the left is a hemisphere. (c) Hence show that the volume of the sphere of radius r is 4/3 π r³.