Expansion of block in a liquid

[zorro]

Homework Statement

A cubical block of coeffficent of linear expansion $$\alpha$$ is submerged partially inside a liquid of coefficient of volume expansion $$\gamma$$. On increasing the temperature of the system by $$\Delta$$T, the height of the cube inside the liquid remains unchanged. Find the relation between $$\gamma$$ and $$\alpha$$

The Attempt at a Solution

Initially,
V_i $$\rho$$_l = V_block$$\rho$$_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.

 

[jbsteele]

If linear expansion of the block is equal to the volume expansion of the liquid,\alpha = \gammaIf areal expansion of the block is equal to the volume expansion of the liquid,3\alpha = \gamma