This one is tougher! An ice cube whose edges measure $20\mathrm{.}0$ mm is floating in a

glass of ice$-$cold water, and one of the ice cube$$s faces is parallel to the water$$s surface.

$($a$)$ How far below the water surface is the bottom face of the block?

$($b$)$ Ice$-$cold ethyl alcohol is gently poured onto the water surface to form a layer $5\mathrm{.}00$

mm thick above the water. The alcohol does not mix with the water. When the

ice cube again attains hydrostatic equilibrium, what is the distance from the top

of the water to the bottom face of the block?

$2$

$($c$)$ Additional cold ethyl alcohol is poured onto the water$$s surface until the top

surface of the alcohol coincides with the top surface of the ice cube $($in hydrostatic

equilibrium$).$ How thick is the required layer of ethyl alcohol?