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Math Help - Finding total surface area of a sphere +more

  1. #1
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    Finding total surface area of a sphere +more

    I have a sphere that is 1.5 inches in diameter thus it has a radius of .75 inches. I have found a formula that gives me the total surface area.

    The formula I found is: 4x3.14x.75^2

    My problem is once I find the total surface area I need to find a way to fit atleast 30 diamonds into that total space. So according to the formula, the total space comes out to 7.065 inches. If this is the case, then I asume that would be a 7.065 by 7.065 flat area? If so how can I figure out how to fit 30 diamonds into that space? So far I have a diamond dimension of .75 inches wide and 2.25 inches long / tall. That comes out to around 27 diamonds.

    40b1t
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  2. #2
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    Quote Originally Posted by 40b1t View Post
    I have a sphere that is 1.5 inches in diameter thus it has a radius of .75 inches. I have found a formula that gives me the total surface area.

    The formula I found is: 4x3.14x.75^2

    My problem is once I find the total surface area I need to find a way to fit atleast 30 diamonds into that total space. So according to the formula, the total space comes out to 7.065 inches. If this is the case, then I asume that would be a 7.065 by 7.065 flat area? If so how can I figure out how to fit 30 diamonds into that space? So far I have a diamond dimension of .75 inches wide and 2.25 inches long / tall. That comes out to around 27 diamonds.

    40b1t
    1. The formula you use is correct:

    A_{surface\ of\ sphere}=4 \cdot \pi \cdot r^2

    With your value of r = 0.75'' you'll get A_{surface\ of\ sphere}=4 \cdot \pi \cdot(0.75)^2\approx 7.0686\ square\ inches

    2. If you transform this area into a square then its side length would be:

    s=\sqrt{7.0686\ square\ inches} \approx 2.659\ inches

    3. Since one diamond is nearly as long as one side of this square you can't place more than 4 diamonds on this area.
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