You are designing a spherical tank to hold water for a small village in a developing country. The volume of liquid it can hold can be computed as
= ℎ
2
[3 − ℎ]
3
where = (3
), ℎ = depth of water in tank (), and = the tank radius ().
If = 3, what depth must the tank be filled to so that it holds 303
?. Use the NewtonRaphson method to determine your answer. Determine the approximate relative error after
each iteration. Note that an initial guess of will always converge.