At sea-level, the barometer which Pie is holding reads 760 mm of Hg. When he is at the top of Mount Pie, the same barometer reads 230 mm of Hg.
Given take the density of mercury to be 13.6 g cm-3 and the density of air, 1.23 x 10-3 g cm-3.
Solutions: 5860 m
Pressure difference in mercury, Pmercury = pgh
= 13600 x 10 x (0.76 – 0.23)
= 72080 Pa
Pressure difference, Pair = pgh
72080 = 1.23 x 10 x h
h = 5860 m
In general, barometer can be used to measure altitude as height increases, height of mercury column will decreases. Of course same calibration has to be done. It is not practical to bring around a mercury barometer as its liquid, heavy and poisonous etc.
An aneroid barometer (no mercury inside though) is used to measure altitude more accurately.