If a barometer was filled with milk (density =1.02 g/ml) rather than mercury, how tall would the barometer have to be to contain this solution?

The barometer is filled with milk instead of mercury. It is assumed that the ambient temperature is 20 C and the barometer is at sea level. The density of milk is 1.02 g/ml, the density of mercury is 13.59 g/ml.

The average air pressure at sea level is 101.325 kPa or 760 mm of Hg. If a barometer were filled with mercury and placed at sea level, the pressure of air would be able to support a column of mercury 760 mm high. As the density of milk is lower than that of mercury, the height of a column of milk that can be supported at the same pressure is going to be higher.

As the density of mercury is 13.59/1.02 = 13.32 times that of milk, the appropriate height of a barometer filled with milk would have to be 760*13.32 = 101.25 cm.

You need a barometer that is 101.25 cm tall to be able to measure atmospheric pressure at sea level using milk instead of mercury.