You work for a process control sensor company. You have developed a float for a level detector.

The float has the shape of an ellipsoid of oblate revolution $($volume obtained by the revolution of an ne ellipse of which $a>b)$

This float of density di will be immersed in a fluid of density $d2.$

The height of the float which is located under the fluid is represented by $H.$

The $H$ data is necessary for the adjustment of the level detector when it is installed by your customers. You offer floats of different densities di and different dimensions $($ a and $b),$ and these can be used for different fluids $($hence different densities d$2).$ You have the mandate to develop the program which gives the ratio of $H$ as a function of the height of the float $($therefore $H$ expressed in a ratio of dimension $2b)$ for a given density of the float di and a given density of the fluid d$2.$