Answer
The volume would increase by $1.44\times 10^{-6}~cm^3$
Work Step by Step
We can find the pressure difference $\Delta P$:
$\Delta P = (10^{-9}~Pa)-(1.01\times 10^5~Pa)$
$\Delta P = -1.01\times 10^5~Pa$
We can find the the change in volume:
$\frac{\Delta V}{V_0} = -\frac{1}{B}~\Delta P$
$\Delta V = -\frac{1}{B}~\Delta P~V_0$
$\Delta V = -\left(\frac{1}{70\times 10^9~Pa}\right)~(-1.01\times 10^5~Pa)(1.00~cm^3)$
$\Delta V = 1.44\times 10^{-6}~cm^3$
The volume would increase by $1.44\times 10^{-6}~cm^3$.
