You are designing a spherical tank (Figure below) to hold water for a small village. The volume of water it can hold can be computed as

where V = volume (m3 ), h = depth of water in tank (m), and R = the tank radius (m). Due to space constraints you have to build the tank with R = 3 m; to what depth must the tank be filled so that it holds 30 m3 ?

A. Develop a python script for the false-position method. It should be similar in structure to the algorithm for bisection, but instead of determining the number of iterations due to the interval width and stopping criterion, create a new condition based on the step-size between the upper and lower brackets. When the step-size (ie the difference between them) drops below some stopping criterion the root estimate is reached.

V = h2 [3R-h]