Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Informal arguments for area formulas can make use of the way in which area scale under similarity transformations: when one figure in the plane results from another by applying a similarity transformation with scale factor k, its area is k² times the area of the first. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
Geometric Measurement and Dimension
- Explain volume formulas and use them to solve problems.