A thin cylindrical vessel of radius $R$, height $H$ and coefficient of linear expansion  $\alpha$ contains a liquid of coefficient of volume expansion  $\gamma$ upto a height of $h$ from the bottom. When the temperature increases by  $\theta$ which  of the following are correct?

Volume of the liquid  $=\left(\pi R^{2}h\right)(1+\gamma \theta )$
Area of the base  $=\pi R^2(1+2\alpha \theta )$
$\therefore$ Height from the bottom  $=\frac{volume}{Area}=h\left(\frac{1+\gamma \theta }{1+2\alpha \theta }\right)$
Depth from the top = height of the cylinder – height of the liquid 

                                $$\begin{gathered} =H(1+\alpha \theta )-h\left(\frac{1+\gamma \theta }{1+2\alpha \theta }\right) \\ =H(1+\alpha \theta )-h(1+(\gamma -2\alpha )\theta ) \end{gathered}$$