Chapter 8, Problem 10P

For the spherical tank in Prob. 8.9, it is possible to develop the following two fixed-point formulas:

$\begin{array}{l}h=\sqrt{\frac{h^3+\left(3V/\pi \right)}{3r}}\\ \text{and }\\ h=\sqrt[3]{3\left(r{h}^2-\frac{V}{\pi }\right)}\end{array}$

If $r=1\text{ m and }V=0.5{\text{ m}}^3$, determine whether either of these is stable, and the range of initial guesses for which they are stable.