Mass of silicon dioxide

I thought I found how many cubic microns were in 1 cubic meter. Why aren't those the units that i'm using?
Then you also found that 1 cubic micron = 1x10^ -18 meters
If you use it in microns wouldn't
m = (2500kg/m3)*1x1018microns3
be in units of kg*micron3/m3
On the other hand:
m = (2500kg/m3)*1x10-18m3
the m3 cancels out in numerator and denominator leaving kg behind.

so the mass of one grain of sand of SiO2 is 2.5x10-15kg
now I need to figure out how many grains of sand with a volume of (4pi(50microns)^3)/3 go into one cubic meter

Last edited:
so i've got 4(2500x10^-18m^3)/3

SteamKing
Staff Emeritus
Homework Helper
so i've got 4(2500x10^-18m^3)/3
Something isn't right. R = 50 microns = 50*10^-6 meters

Volume = (4/3)pi*R^3 = (4/3)*pi*(50*10^-6)^3 m^3 / grain of sand

Surface Area = 4*pi*R^2 = 4 * pi * (50*10^-6)^2 m^2 / grain of sand

Sand has a density of 2500 kg / m^3

You want to find out:

1. how many grains of sand have a total surface area of 6 m^2, and then
2. how many kg of sand this is equivalent to.

Knowing the surface area of 1 grain of sand, how many grains have a total surface area of 6 m^2?

Knowing how many grains of sand, what is the total volume of sand?

Knowing the total volume of the sand, what is its mass?

Answer these questions, and you will have solved the problem from the OP.