Mercury is often used as an expansion medium in a thermometer. The mercury sits in a bulb on the bottom of the thermometer and rises up a thin capillary as the temperature rises. Suppose a mercury thermometer contains 3.250 g of mercury and has a capillary that is 0.180 mm in diameter. How far does the mercury rise in the capillary when the temperature changes from 0.0 ∘C to 25.0 ∘C? The density of mercury at these temperatures is 13.596 g/cm3 and 13.534 g/cm3, respectively.

Let's first obtain the volume at both temperatures using the relationship Volume = Mass/Density. 
At 0 degrees C (V_1e have:
V_1 = (3.250 g)/(13.596 g/(cm^3)) = .2390 cm^3
At 25 degrees C (V_2e have:
V_2  = (3.250 g)/(13.534 g/(cm^3)) = .2401 cm^3 
We will think of the column of mercury inside the capillary as a cylinder. The height of the cylinder is given by the formula
h = V/(pi * r^2)
The radius, r, in centimeters is (0.180 mm) / 2 * (1 cm)/(10 mm) or .009 cm. Therefore, at 0 degrees, the height is:
h_1 =(.2390 cm^3)/(pi*(.009 cm)^2)  = 939.2 cm

At 25 degrees C, the height is:
h_2 =(.2401 cm^3)/(pi*(.009 cm)^2) = 943.5 cm
Subtracting these two, 943.5 cm - 939.2 cm, we obtain a rise in mercury height of 4.3 cm, the final answer. 
https://en.wikipedia.org/wiki/Density

https://www.mathopenref.com/cylindervolume.html