A76 pound flask a mercury cost $126 the density and mercury is 13.534 g/cm³ find the price of one cubic inch of mercury by calculating the following intermediate values

To determine the cost of the mercury per cubic inch, we need to divide the total cost with the total volume in units of cubic inches. To do this, we first determine the volume of the mercury given the mass and the density. In any operation, it is important to remember that the units of the values involved should be homogeneous so that we can cancel them. We do as follows:

mass of mercury = 76 lb ( 1 kg / 2.2 lbs ) ( 1000 g / 1 kg ) = 34545.45 g
volume of mercury in cm^3 = 34545.45 g / 13.534 g / cm^3 = 2552.49 cm^3

We need to convert this to units of cubic inches since it is what is asked.

volume of mercury in in^3 = 2552.49 cm^3 ( 1 in / 2.54 cm )^3 = 155.76 in^3
cost per in^3 = $126 / 155.76 in^3 = $ 0.809 / in^3