#### Answer

(a) The amount of water that spills over the top of the glass is $1.47~mL$
When the expansion of the glass is not considered, the amount of water that spills over the top of the glass is $1.69~mL$
(b) When the expansion of the glass is considered, the answer decreases by 13%

#### Work Step by Step

(a) We can find the change in volume of the glass due to the increase in temperature:
$\Delta V = \beta~\Delta T~V$
$\Delta V = (27\times 10^{-6}~K^{-1})(30.0~K)(268.4~mL)$
$\Delta V = 0.217~mL$
We can find the change in volume of the water 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 $1.69~mL-0.217~mL$ which is $1.47~mL$
When the expansion of the glass is not considered, the amount of water that spills over the top of the glass is $1.69~mL$
(b) We can find the fraction that the answer changed:
$\frac{1.47~mL-1.69~mL}{1.69~mL} = -0.13$
When the expansion of the glass is considered, the answer decreases by 13%