The volume V of a spherical tank of radius r is related to the depth of the liquid h by
V = πh²(3r - h) / 3
Use this function for r = 1 m and V = 0.5 m³ and the data provided in the table below to determine:
a) The roots of the equation using Bisection, Newton-Raphson and Secant method.
b) The value of f(V) at h = 1.5 m using Newton divided difference (NDD) and Lagrange interpolation.
c) The radius r as unknown after best fitting the curve to above equation.
Table Data:
h: 0.7, 0.8, 0.9, 1.0, 2.0, 3.0, 4.0
f(h): 0.680192, 0.974454, 1.281283, 1.594395, 3.688790, -0.50000, -17.2552