Question

Grains of fine beach sand are approximately spheres with an average radius of 50 micro meter and are made of silicon di oxide, which has a density of 2600 kg/m ³. What mass of sand grains would have a total surface area ( the total area of all the individual spheres) equal to the surface area of a cube 1m on an edge?

Answer 1

Surface area of a sand = 4 π X R² m²
R = 50X10^-6 m
Total surface of a cube of 1 m edge = 6X(1m)² = 6 m²

Number of sand particle which have 6 m² surface area = 6/(4 π R² )

Total volume (V) of sand is = 6/(4 π R² ) X [4/3 π X R³ ] = 2R
Mass of sand particles = volume (V) X density (d)
= 2R X 2600 kg/m³
= 2 X (50X10^-6 m) X 2600 kg/m³
= 0.26 kg