Measuring Liquid Volume:

The volume of a liquid sample is generally measured by means of a test tube or flask marked off in milliliters or liters. Though, there is another way to measure the volume of a liquid sample, given we know its chemical composition and the weight density of the substance in question. This is to weigh up the sample of liquid and then divide the weight by the weight density. We should, of course, pay extra care to the units. In specific, the weight should be expressed in newton that is equal to the mass in kilograms times the acceleration of gravity (9.81 m/s²).

Let us do a mathematical work out to show why we can measure volume in this way. Assume d_w be the known weight density of a enormous sample of liquid too large for its volume to be measured by using a flask or test tube. Assume that this substance has a weight of w, in newtons. When V is the volume in meters cubed, we have the formula,

d_w = w/V

since w = ma, here a is the acceleration of gravity. When we divide both sides of this equation by w, we acquire

d_w/w = 1/V

Then we can upturn both sides of this equation and swap the left-hand and the right-hand sides to acquire,

V = w/dw

All this is based on the hypothesis that V, w, and d_w are all nonzero quantities. This is forever true in the real world; all materials take place at least some volume, contain at least some weight since of gravitation, and contain some density as there is some "material" in a limited amount of physical space.