A cylinder of radius a and height L is aligned with the z axis. The surface differential of the sidewall is given by ds = r d phi dz r. Show that the surface area of the sidewall is given by is S = 2 pi aL. The surface differential of a sphere of radius a is given by ds = R^2 sin theta d theta d phi R. Show that the surface area of the sphere is S = 4 pi a^2. In spherical coordinates, the volume differential is given by dV = R^2 sin theta dR d theta d phi. Assume that a sphere of radius a is centered at the origin. show that the volume is V = 4/3 pi a^3.
