Help!!! Physics question involving grains of sand and surface area.?

Question

Here is the question:

Fine grains of beach sand are assumed to be spheres of radius 51.1 um (micrometer). Theses grains have a density of 2600 kg/m^3.

What is the mass of each grain of sand???

Answer 1

First calculate the volume of the grain of sand:

Let's first convert to m since the density is in meters.

1 meter= 1x10^6 micro meters

So 51.1 um= 51.1 x 10^-6 m

The volume of a sphere is V= 4/3 pi r^3

Once you have the volume use the density equation:

D=M/V

M=V x D

4/3 x pi x (51.1 x 10^-6 m)^3 x (2600 kg/m^3)=0.428 kg or 428.1g