write a python code.

Write a python code for the problem below.

According to Archimedes principle, the buoyancy force is equal to the weight of fluid displaced by the submerged portion of an object. The sphere below has a radius of $1$ m and a density $({}_s)$ of $200k\frac{g}{m^3}.$ The water has a density $({}_w)$ of $1000k\frac{g}{m^3}.$ Note that the volume of the above water portion of the sphere can be computed as:

$V=\frac{h^2}{3}(3r-h)$

Use a force balance between the sphere weight and the buoyancy force. Formulate the problem as a root problem. Then, create a while loop program using Newton's method with an initial guess value of $0\mathrm{.}4$ m $,$ determine the height $h$ of the portion that is above water. Continue performing iterations until the solution converges to $6$ decimal places. State the converged value of $h$ and the number of iterations required to converge. Plot the iterations of $h$ to show convergence.

Verify your answers by plugging result back into original equation.