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Math Help - Physics calc/surface area

  1. #1
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    Physics calc/surface area

    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 2.8 103 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 1.1 m on an edge?

    I have calculated the surface areas of the sand but i am stumped from there on... please help.
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  2. #2
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    \mbox{Surface Area of N grains of sand}= 4 \pi r^2 N (1)

    \mbox{Surface Area of a 1.1m edge cube} =6 \cdot 1.1^2 (2)

    \mbox{Mass of N grains of sand} = \mbox{Density of sand} \cdot \mbox{Volume of N grains of sand} (3)

    \mbox{Volume of N grains of sand} = \frac{4}{3} \pi r^3 N (4)

    So, (1)=(2):

    4 \pi r^2 N = 6 \cdot 1.1^2

    N = \frac{3 \cdot 1.1^2}{2\pi r^2} (5)

    Now we compute the volume using (4) and replacing N with (5):

    Volume = \frac{4 \pi r^3 \cdot 3 \cdot 1.1^2}{3 \cdot 2 \pi r^2}

    Volume = 2 r \cdot 1.1^2 (6)

    Finally we compute the mass using (3) and (6):

    Mass = 2.8 \cdot 10^3 \cdot 2 r \cdot 1.1^2

    Be aware that I assume r is in meters (therefore you'll have to convert 50 micrometers to meters), the final mass comes in kg.
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