The volume of water a spherical tank can hold is given by the next formula:
● V is the water volume inside the tank in
● R is the radius in , and
● h is the level of water, measured from the bottom of the tank (in ).
I need to find out, using bisection and Newton-Raphson iterations, what the level of water has to be in order to get of water from a radius tank.
So basically, what i've done is find the value of within the formula, and apply bisection to the resulting equation. But here's the problem. The resulting formula is a 3º degree formula, so i get 3 roots (obviously bisection gives me just one, depending on the initial interval).
So the three roots are (aprox.):
Thanks in advance.
P.S.: I'm using scilab as my numerical analysis software.