posted by SARA on .
Grains of fine California beach sand are approximately spheres with an average radius of 50 μm and are made of silicon dioxide, which has a density of 2.4 × 103 kg/m3. 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 1.1 m on an edge?
The area of that cube would be 1.1^3 = 1.331 m^3.
If that is the total surface area of sand grains with radius 50*10^-6 m, the number N of sand grains would be given by
N*4*pi*(50^10^-6)^2 = 1.331
N = 4.23*10^7 grains
Each sand grain has a mass m given by
(4/3)*pi*(50*10^-6)^3*2400 = 1.273^10^-10 kg/grain
The mass of the N sand grains with an area of 1.331 m^3 is
5.4*10^-3 kg = 5.4 grams
Check my thinking and calculations.