To solve this problem we will proceed to calculate the specific volume from the area of the cylinder and the sensitivity. Later we will calculate the volumetric coefficient of thermal expansion and finally we will be able to calculate the volume through the relation of the two terms mentioned above. Our values are



Let's start by calculating the specific volume which is given by

Here,
d = Diameter
= Sensitivity
Replacing our values we have


Now we will obtain the value of the volumetric coefficient of thermal expansion of mercury through the differential expansion coefficient of Hg whic is three times, then



Finally the relation to calculate the volume the bulb must is





Therefore the volume that the bulb must have is 