# G.GGMD.3 Volume of Spheres

- Author:
- Dan Dale, Anthony OR 柯志明

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*r*³.