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 h 2 3R h 3 Where V volume ft 3 , 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...

The equation to be solved is Because this equation i ...

You are designing a spherical tank (Figure) to hold water for a small village in a developing

Question:

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.