Excess pressure, $\Delta P_1=1.01 \mathrm{atm}-1 \mathrm{atm}=0.01 \mathrm{atm}$ and similarly, $\Delta P_2=0.02 \mathrm{atm}$ and

The volume of the air bubble $V=\frac{4}{3}\pi r^3$

Therefore, $V\propto r^3\propto \left[\frac{1}{(\Delta P{)}^3}\right]$

As $\Delta P\propto \left(\frac{1}{r}\right) \mathrm{or} r\propto \left(\frac{1}{\Delta P}\right)$

$\frac{V_1}{V_2} = {\left(\frac{\Delta P_2}{\Delta P_1}\right)}^3={\left(\frac{0.02}{0.01}\right)}^3 = 8$