Question

f fine California beach sand are approximately spheres with an average radius of 42 μ m and are made of silicon dioxide. A solid cube of silicon dioxide with a volume of 1.00 m2 has a mass of 2600 kg. What mass of small sand grains would have a total surface area (the total area of all individual spheres) equal to the surface area of a cube 1.00 m on an edge? Submit Answer Tries o/8

Answer 1

average radius of sphere R= 42 micrometer =42*10^-6m

mass of solid cube m = 2600kg

volume of cube V= 1 m^3

relation between volume and mass

m= $\rho$V---------(1)

2600= $\rho$*1

$\rho$= 2600kg/m^3= 26*10^2 kg

where $\rho$ is density of sphere and V is volume

we also know that for sphere  

V= 4/3*(πR^3)---------(2)

from (1) and (2)

m= 4/3*(π$\rho$R^3)

m= 4/3{3.14* 26*10^2*(42*10^-6)^3}

m= 8.06*10^-10kg