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 \(r\), \(V=\frac{4}{3}\pi r^3\)