Rising bubble

The pressure and volume of the bubble when it is at the bottom of the pond are:

$p_1=p_A+\rho g h+\frac{2\sigma}{r}=p_A+\rho g h+\frac{4\sigma}{d}$

$V_1=\frac{4}{3} \pi r^3$ .

The pressure and volume of the bubble when it rises to the surface are:

$p_2=p_A+\frac{2\sigma}{r'}=p_A+\frac{4\sigma}{nd}$

$V_2=\frac{4}{3} \pi n^3 r^3$ .

Since the gas expansion is isothermal, we have: $p_1V_1=p_2V_2$

Therefore, $p_A+\rho g h+\frac{4\sigma}{d}=n^3 (p_A+\frac{4\sigma}{nd})$ .

So, $h=\frac{n^3 (p_A+\frac{4\sigma}{nd})-(p_A+\frac{4\sigma}{d})}{\rho g}=4.94(m)$ .