A metallic sphere $($initial radius r$0,$ density $$s$)$ is suspended above a cylindrical tank already containing

the same metal in liquid state $($density $$l$).$ The tank$\text{'}$s diameter is D and the initial level of the liquid

metal in the tank is h$0.$ The sphere is melting slowly, and its diameter is decreasing at a constant rate

$\backslash$alpha $($m$/$s$).$

Determine:

$($a$)$ the expression for the variation of the sphere's radius with time,