Question 1174168: You are working with an Engineers without Borders team to produce a small water treatment facility in Guatemala using a simple sand filter. The system's filtering ability is roughly proportional to the surface area of the filter's sand particles. You model the sand grains as approximately spheres with an average radius of 50 μm and are made of silicon dioxide. A solid cube of this material with a volume of 1 m3 has a mass of 2550 kg. You have determined that the total surface area of all the sand grains is equal to the surface area of a cube 1.2 meters on an edge. What mass of grains are needed for your filter?
I do not know how to solve this problem. I don't know which information to use either. I think I'll have to set up a proportion at some point. I tried solving the surface area of a 1.2 meter cube and taking the proportion with respect to the cube with an edge of 1 meter, and multiplying this by 2550, but this answer was incorrect. Any help would be greatly appreciated.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The radius is 50 x 10^(-6) m, 5 x 10^(-5)m and the volume is (4/3)*π*125 x(10^-15)m^3
=523.6*10^(-15)m^3, or 5.236 x 10^(-13 )m^3
1 m^3/2550 kg =5.236 *10^-13/x; also, 2.55 x 10^3 kg= 2.55 x 10^6 gm
1 m* x=13.35 x 10^(-7) gm or 1.335 x (10^-6) gm., the mass of each grain.
--
total surface area of one sand grain is 4*π*r^2=4π(25 x 10^-10)=3.142 x 10*(-8) m^2
surface area of a cube 1.2 m on an edge is 1.2*1.2*6=8.64 m^2
the number of grains would then be 8.64/3.142 x 10^-8
=2.75 x 10^8 grains.
each grain has 1.335 x 10^(-6) gm mass/grain, so the product would be 3.671 X 10^2 or 367 gm of sand.
|
|
|
