The surface area of a sphere of radius r is 4r 2 . Use this to derive

The surface area of a sphere of radius r is 4πr². Use this to derive the formula for the volume V of a sphere of radius R in a new way.
(a) Show that the volume of a thin spherical shell of inner radius r and thickness Δr is approximately 4πr²Δr.
(b) Approximate V by decomposing the sphere of radius R into N thin spherical shells of thickness Δr = R/N.
(c) Show that the approximation is a Riemann sum that converges to an integral. Evaluate the integral.