Archimedes revisited: a faster, better, cheaper method of accurately measuring the volume of small objects

TLDR

The suspension technique is a variation on the hydrostatic weighing technique used for measuring volume. The study describes a little‑known Archimedes‑based method that measures the volume of small objects by suspending them in a water‑filled container on electronic scales. The authors compared the suspension method with two traditional water‑displacement techniques—level rise in a measuring cylinder and overflow spout—using ten PVC cylinders (1.5–15.7 ml) and repeated each measurement twice to assess accuracy, precision, and reproducibility. The suspension method achieved a mean difference of 0.03 ± 0.45 % and reproducibility of –0.04 ± 0.43 %, outperforming the level (3.3 ± 7.3 %/–1.7 ± 8.5 %) and overflow (–1.6 ± 7.2 %/0.09 ± 3 %) techniques and surpassing Vernier caliper measurements.

Abstract

A little-known method of measuring the volume of small objects based on Archimedes' principle is described, which involves suspending an object in a water-filled container placed on electronic scales. The suspension technique is a variation on the hydrostatic weighing technique used for measuring volume. The suspension method was compared with two other traditional water displacement methods of measuring volume, i.e. placing an object in a measuring cylinder and recording the rise in the water level and immersing the object in a water-filled container with an overflow spout to record the volume of overflow. The accuracy and precision of the three methods was compared using ten accurately machined PVC cylinders ranging in volume from 1.5 to 15.7 ml. The mean difference between the actual and measured volumes was 3.3 ± 7.3%, -1.6 ± 7.2% and 0.03 ± 0.45%, for the level, overflow and suspension methods respectively. Each measurement was repeated twice to obtain the reproducibility of the three displacement techniques. The reproducibility was -1.7 ± 8.5%, 0.09 ± 3% and -0.04 ± 0.43% for the level, overflow and suspension techniques respectively. The results show that the suspension technique is more accurate and precise than the traditional water displacement methods and is more accurate than measuring volume using Vernier calliper measurements.