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:$1.3\times10^{-9}kg$

Volume of each grain of sand:

$V=\frac{4}{3}\pi r^3$

radius of the spherical grain is given,$r=49.8\mu m=49.8\times10^{-6} m$

$\Rightarrow V=\frac{4}{3}\times3.14\times(49.8\times10^{-6})^3m^3=5.17\times10^{-13}m^3$

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:

$Mass=Density (D)\times Volume(V)\\ \Rightarrow M=2600 kg/m^3\times5.17\times10^{-13}m^3 =1.3\times10^{-9}kg$