Question

Grains of fine California beach sand are approximately spheres with an average radius of 50 μm and are made of silicon dioxide, which has a density of 2.7 × 103 kg/m3. 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 0.8 m on an edge?

Answer 1

The mass of sand grains is
`1.413*10^(-9)\ kg`

Step-by-step explanation:

Given that,

Radius
`r = 50\ mu m`

Density
`\rho=2.7*10^(3)\ kg/m^3`

Cube edge = 0.8 m

We need to calculate the mass of sand grains

Using formula of density

`\rho = (m)/(V)`

`m=\rho* V`

Where,
`\rho` = density

V = volume

Put the value into the formula

`m =2.7*10^(3)*(4)/(3)\pi*r^3`

`m=2.7*10^(3)*(4)/(3)*3.14*(50*10^(-6))^3`

`m=1.413*10^(-9)\ kg`

Hence, The mass of sand grains is
`1.413*10^(-9)\ kg`