SUMMARY
The mass of a grain of beach sand, modeled as a sphere with a radius of 38.1 micrometers and composed of silicon dioxide with a density of 2600 kg/m³, can be accurately calculated using the formula for the volume of a sphere and the relationship between mass, volume, and density. The correct calculation involves converting the radius to meters, calculating the volume in cubic meters, and then applying the density to find the mass. The error in the initial calculations stemmed from incorrect unit conversion of density from kg/m³ to kg/μm³.
PREREQUISITES
- Understanding of the volume formula for a sphere: V = (4/3)πr³
- Knowledge of unit conversion, particularly between cubic meters and cubic micrometers
- Familiarity with density and its relationship to mass and volume
- Basic algebra skills for manipulating equations
NEXT STEPS
- Learn about unit conversion techniques, especially for cubic measurements
- Study the properties of silicon dioxide and its applications in material science
- Explore the mathematical derivation of the volume of a sphere
- Investigate common errors in density calculations and how to avoid them
USEFUL FOR
Students in physics or chemistry courses, educators teaching material properties, and anyone interested in understanding the calculations related to small particle mass and density.