Answer
The amount of water that spills over the top of the glass is $1.69~mL$
Work Step by Step
We can find the change in volume due to the increase in temperature:
$\Delta V = \beta~\Delta T~V$
$\Delta V = (210\times 10^{-6}~K^{-1})(30.0~K)(268.4~mL)$
$\Delta V = 1.69~mL$
The amount of water that spills over the top of the glass is $1.69~mL$
