MEASURING LIQUID VOLUME

The volume of a liquid sample is usually measured by means of a test tube or flask marked off in milliliters or liters. However, there’s another way to measure the volume of a liquid sample, provided we know its chemical composition and the weight density of the substance in question. This is to weigh the sample of liquid and then divide the weight by the weight density. We must, of course, pay careful attention to the units. In particular, the weight must be expressed in newtons, which is equal to the mass in kilograms times the acceleration of gravity (9.81 m/s²).
Let’s do a mathematical exercise to show why we can measure volume in this way. Let dw be the known weight density of a huge sample of liquid too large for its volume to be measured using a flask or test tube. Suppose that this substance has a weight of w, in newtons. If V is the volume in meters cubed, we know from the preceding formula that
dw = w/V
because w = ma, where a is the acceleration of gravity. If we divide both sides of this equation by w, we get
dw/w = 1/V
Then we can invert both sides of this equation and exchange the left-hand and the right-hand sides to obtain
V = w/dw
All this is based on the assumption that V, w, and d_w are all nonzero quantities. This is always true in the real world; all materials occupy at least some volume, have at least some weight because of gravitation, and have some density because there is some “stuff” in a finite amount of physical space.