A glass flask holds exactly $500\ \text{cm}^3$ and is filled to the brim with mercury at $20^\circ\text{C}$. The flask and the mercury are heated together to $100^\circ\text{C}$. The coefficient of volume expansion of mercury is $1.8 \times 10^{-4}\ \text{K}^{-1}$, and the coefficient of linear expansion of the glass is $9 \times 10^{-6}\ \text{K}^{-1}$. The volume of mercury that spills out is closest to