Expansion of block in a liquid

Abdul Quadeer

1. The problem statement, all variables and given/known data
A cubical block of coeffficent of linear expansion [tex]\alpha[/tex] is submerged partially inside a liquid of coefficient of volume expansion [tex]\gamma[/tex]. On increasing the temperature of the system by [tex]\Delta[/tex]T, the height of the cube inside the liquid remains unchanged. Find the relation between [tex]\gamma[/tex] and [tex]\alpha[/tex]


3. The attempt at a solution

Initially,
V_i [tex]\rho[/tex]_l = V_block[tex]\rho[/tex]_block

After heating, the height of the immersed part of the block remains unchanged. For this to happen, I don't understand whether the linear expansion or areal expansion of the block
should be equal to the volume expansion of the liquid.