The surface area of a sphere of radius r is 4 r2. Use this to derive the formula for the
Chapter 6, Problem 60(choose chapter or problem)
The surface area of a sphere of radius r is 4 r2. 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 r is approximately 4 r2r. (b) Approximate V by decomposing the sphere of radius R into N thin spherical shells of thickness r = R/N. (c) Show that the approximation is a Riemann sum that converges to an integral. Evaluate the integral.
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