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Homework Help: Surface area of basket ball full of sand

  1. May 10, 2010 #1
    1. The problem statement, all variables and given/known data
    A regulation NCAA basketball is a sphere of radius approximately 12 cm. Grains of Texas beach sand are
    approximately spheres of radius 25 μm. If the inside volume of a basketball were completely filled with sand
    (assume perfect packing with no empty space) what is the approximate total surface area, in m2, of all of the
    sand grains?

    2. Relevant equations

    area of circle = pi(r)^2
    surface area = 4pi(r)^2
    volume = 4pi/3(r)^3
    nanometers = 1/10^6 meters
    centimeters = 1/10^2 meters

    3. The attempt at a solution

    I have tried to solve for this by finding the volume of the basketball then finding the surface area of a single grain. I then took the volume of the basket ball and divided it by the area of a single grain to see how many would fit, once i got that number i multiplied it by the surface area of one grain of sand for the total surface area. I made sure to convert all the units to their proper places and amounts but still no luck. Please help i have a final tomorrow and i can't figure this one out i have spent hours on it, thank you.
  2. jcsd
  3. May 10, 2010 #2
    Find the volume of the basketball and the volume of a grain of sand, then find how many grains of sand would fit in if they were perfectly packed. Find the surface area of a single grain... missing the last step... good enough?
  4. May 10, 2010 #3
    so your saying divide the volume of the basketball by the volume of a grain? then multiply that by the surface area of a grain?
  5. May 10, 2010 #4
    Yep. Make sense?
  6. May 10, 2010 #5
    Find how many grains of sand will fill the basketball (you need to find the volume of each). Find the surface area of a grain of sand. Multiply.
  7. May 10, 2010 #6
    Thank you so much guys really appreciate it
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