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## Homework Statement

As part of the initial treatment for waste water from an industrial site, you will be running the afluent through a sand filter. The filtering ability of the sand in this filter is roughly proportional to the surface area of the sand enclosed. The grains of fine sand are 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 m

^{3}has a mass of 2500 kg. You have determined that the total surface area (the total area of all the individual grains) is equal to the surface area of a cube 1 meters on an edge.

What is the mass of the sand in kilograms

## Homework Equations

Volume of sphere

Surface Area of Cube

## The Attempt at a Solution

The Volume of a sphere is (4pir

^{3})/3 and the surface area of a cube is 4a

^{2}and the surface area of a cube 1 meter on an edge is 1m

^{3}I also have the number of particles in a sphere (4/3)pi(50μm)

^{3}and I have 6m

^{2}/(4pi(50μm)

^{2})

I don't know what this information is doing geometrically or what it has to do with finding the mass of the sand but it was written down and I needed help filling in the blanks.

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