You are designing a spherical tank (Figure) to hold water for a small village in a developing country. The volume of liquid it can hold can be computed as V = ?h² [3R + h]/3. Where V = volume [ft³], h = depth of water in tank [ft], and R = the tank redius [ft].

If R = 3 m, what depth must the tank be filled to so that it holds 30 m³? Use three iterations of the Newton-Raphson method to determine your answer. Determine the approximate relative error after each iteration. Note that en initial guess of R will always converge.

Fab R h