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Silicon Dioxide surface area

  1. Aug 29, 2012 #1
    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 2.6 × 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?


    2. The attempt at a solution

    1) First, find the surface area of the cube:
    A = 6s² = 6 * (1.1 m)² = 7.26 m²
    2) Next, find the surface area of one sand grain:
    A = 4∏r² = 4∏ * (50 µm)² = 31,416 µm²
    3) How many grains of sand equal the area of the cube.
    7.26 m²/ 31,416 µm² * (1,000,000 µm/m)² = 231,092,437 grains of sand
    4) Find the volume of one grain of sand.
    V = (4/3)∏r³ = (4/3)∏(50 µm)³ = 523,599 µm³
    5) How many grains of sand is in that cube weigh 2600 kg.
    1.00 m³/523,598 µm³ * (1,000,000 µm/m)³ = 1,909,859,228,000 pieces of sand weighs 2600 kg
    6) How much does each piece of sand weigh.
    2600 kg/1,909,859,228,000 pieces * 1000 g/kg = 1.36E-6 g
    7) How much does 231,092,437 grains of sand weigh?
    1.81 E -6 g * 231,092,437 = 315 g

    Okay, now the problem is that it says my answer is wrong!? I must have done something wrong. I'm thinking that maybe in step 5 where I rounded the last 1,909,859,228,"000" three digits off. Is this that big of a problem to throw my answer off? If not can you help me find what I did wrong?
     
  2. jcsd
  3. Aug 29, 2012 #2

    phyzguy

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    I didn't check it all, but the logic looks correct. However, you multiplied wrong in step 7.
    1.81*2.31 = 4.18
     
  4. Aug 29, 2012 #3
    Wait why would I do that?
     
  5. Aug 30, 2012 #4

    phyzguy

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    Science Advisor

    I'm saying that in your last step, 1.81 E -6 g * 231,092,437 = 418g, not 315g.
     
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