Today we saw how to use a definite integral to calculate the volume of a solid of revolution. (Some textbooks will refer to this as finding a “volume of revolution.”)
The solid we studied today is shown below, and the equation used to generate this solid was y=\cos x +2, with x running from 0 to 5. Can you use your knowledge of solids of revolution to derive the formulas for
- the volume of a cone with height h and a base of radius r, V=\frac{1}{3}\pi r^2h
- the volume of a sphere of radius r, V=\frac{4}{3}\pi r^3