Question

Fine grains of beach sand are assumed to be spheres of radius 49.8 µm. these grains are made of silicon dioxide which has a density of 2600 kg/m 3 . what is the mass of each grain of sand? answer in units of kg.

Answer 1

Answer:
`1.3*10^(-9)kg`

Volume of each grain of sand:

`V=(4)/(3)\pi r^3`

radius of the spherical grain is given,
`r=49.8\mu m=49.8*10^(-6) m`

`\Rightarrow V=(4)/(3)*3.14*(49.8*10^(-6))^3m^3=5.17*10^(-13)m^3`

The grains are made up of silicon dioxide.

The density is equal to
`D=2600 kg/m^3`

Then, the mass of each grain is given by:

`Mass=Density (D)* Volume(V)\\ \Rightarrow M=2600 kg/m^3*5.17*10^(-13)m^3 =1.3*10^(-9)kg`