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:

V = πh^2  [3R - h]/3

where V = volume [m3], h = depth of water in tank [m], and R = the tank radius [m]. If R = 3 m, to what depth must the tank be filled so that it holds 30 m3?

1.Fixed-Point Iteration (check for convergence criteria)

2.Using the Newton-Raphson method (xi = 1).

3.Using the Secant method (xi–1 = 1 and xi = 1.5).

4.Using the Modified Secant method (xi = 1.5, δ = 0.01).

Determine the approximate relative error after each iteration.