Pyramids and spheres (English subtitles available)

Through a simple experiment, it is demonstrated that the water contained in a prism is three times the water contained in a pyramid with the same base and height. This shows that the volume of a pyramid is one third of the volume of a prism with the same base and height. The programme uses a pyramid with a rectangular base as an example to illustrate the calculation of the volume of a pyramid. By comparing the material used for making a pyramid and a prism with the same base and height, the calculation of the surface area of a pyramid is demonstrated. It also points out that the difference in their volume is much greater than the difference in their surface areas. The programme highlights the special shape of a circular cone when it is spread out flat. The formula for the curved surface area of a circular cone is introduced. It also shows the relation between a frustum and a pyramid. The method of calculating the volume and surface area of a frustum is clearly elaborated with an example. Finally, the programme puts forward a scenario of save the environment to introduce the formulas for the volume and surface area of a sphere and their applications.
Please click here for the Chinese version.