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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 2.4 × 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?

  • PHYSICS - ,

    The area of that cube would be 1.1^3 = 1.331 m^3.
    If that is the total surface area of sand grains with radius 50*10^-6 m, the number N of sand grains would be given by
    N*4*pi*(50^10^-6)^2 = 1.331
    N = 4.23*10^7 grains

    Each sand grain has a mass m given by
    (4/3)*pi*(50*10^-6)^3*2400 = 1.273^10^-10 kg/grain

    The mass of the N sand grains with an area of 1.331 m^3 is
    5.4*10^-3 kg = 5.4 grams

    Check my thinking and calculations.

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