# Thread: Help with volume formula

1. ## Help with volume formula

The volume of water a spherical tank can hold is given by the next formula:

$\displaystyle V(h)= \pi h^2 \frac{3R - h}{3}$

, where:

● V is the water volume inside the tank in $\displaystyle m^3$
● R is the radius in $\displaystyle m$, and
● h is the level of water, measured from the bottom of the tank (in $\displaystyle m^3$).

I need to find out, using bisection and Newton-Raphson iterations, what the level of water has to be in order to get $\displaystyle 90m^3$ of water from a $\displaystyle 3m$ radius tank.

So basically, what i've done is find the value of $\displaystyle h$ 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.):
●$\displaystyle 7.4526264$
●$\displaystyle 4.2565863$
●$\displaystyle - 2.7092127$

P.S.: I'm using scilab as my numerical analysis software.

2. What is your question? It looks like you have the solution right there.

3. Sorry, stupid me.. the tank is 3m in radius, so the 7.54(something) root is irrelevant.

Thanks anyways.