# Volume of Spheres with Proof

- Author:
- Anthony OR 柯志明

- Topic:
- Solids or 3D Shapes, 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) Are the cross-sections equal in area? (c) Hence show that the volume of the sphere of radius*r*is 4/3 π*r*³.