1. The problem statement, all variables and given/known data
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 2.5 × 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 0.9 m on an edge?
2. Relevant equations
density=mass/volume
surface area of sphere=4(pi)r^2
volume of sphere= (4/3)(pi)r^3
3. The attempt at a solution
My attempt at the solution was i plugged 0.9 into the surface area equation and solved for the value r which gives the surface area equaled to 0.9. I then used the r that i calculated for and plugged that into the volume equation to get the value of V to then plug that into the density equation to find the mass using the given density of the sand and the volume from what i calculated. I do not know where the 0.5μm and i think that is the problem i am having. FInal answer i got was 200kg?
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 2.5 × 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 0.9 m on an edge?
2. Relevant equations
density=mass/volume
surface area of sphere=4(pi)r^2
volume of sphere= (4/3)(pi)r^3
3. The attempt at a solution
My attempt at the solution was i plugged 0.9 into the surface area equation and solved for the value r which gives the surface area equaled to 0.9. I then used the r that i calculated for and plugged that into the volume equation to get the value of V to then plug that into the density equation to find the mass using the given density of the sand and the volume from what i calculated. I do not know where the 0.5μm and i think that is the problem i am having. FInal answer i got was 200kg?
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