Help writing a python code For the given problem

HW$3\_2$ According to Archimedes, if a solid that is lighter than a fluid is placed in the fluid, the solid will

be immersed to such a depth that the weight of the solid is equal to the weight of the displaced fluid:

${}_s{V}_s={}_w{V}_w$

The volume of the displaced water $V_w=(h^{2}r-\frac{h^3}{3}),$ where $h$ is the height of the water, measured

from the bottom of the spherical cork of volume $V_{S^{\text{'}}}.$

Find the floating depth $h$ for a cork ball of radius $4$ cm whose density $({}_s)$ is one quarter that of water

$({}_w)$ using Newton$-$Raphson method to an accuracy of $3$ sig figs. $[$ Use CGS units$].$

Hints:

The density of water $({}_w)=1g\frac{m}{c}c$

Volume of spherical cork of radius $r,V_s=\frac{4}{3}{r}^3$