anyone good in physics? help please?

Question

grains of fine california beach sand are approximately spheres with an average radius of 50 um (micro-meters = 10^6) and are made of silicon dioxide. A solid cube of silicon dioxide with a volume of 1.00 m^3 has a mass of 2600 kg. 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 1.00m on an edge?

Answer 1

1) The density of silicon dioxide is found from the mass of the solid cube. D = 2600 kg/m^3.

2) The surface area of each sand grain Sg is 4πr^2 = 4*(50*10^-6)^2*π

3) The surface area of a cube 1.00m on edge is 6m^2 (six faces on a cube, each 1m x 1m).

4) The number of grains to equal that surface area is 6 / [4*(50*10^-6)^2*π]

5) The mass of each grain is density of SiO2 times the volume of each grain. The volume of each grain = (4/3)πr^3 = (4/3)(50*10^-6)^3*π. The mass of each grain is then 2600*(4/3)(50*10^-6)^3*π kg.

6) The total mass of the grains is then the number of grains times the mass of each

6 / [4*(50*10^-6)^2*π] * 2600*(4/3)(50*10^-6)^3*π kg

This simplifies to 2*2600*50*10^-6 kg

Answer 2

That depends on the temperature of the sand.