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Math Help - Surface Area

  1. #1
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    Surface Area

    Many countries extend their borders by making a claim over territorial waters inside a defined km distance from their coastline.
    What is the size (radius and area) of a circular island claiming a territorial waters of limit of 40km whose landmass is 75% of all territories claimed? Describe your method of finding a solution.

    Could someone please show me the working out?










    Answer: r=259km, area=210 026km^2
    Thanks
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  2. #2
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    Quote Originally Posted by Fibonacci View Post
    Many countries extend their borders by making a claim over territorial waters inside a defined km distance from their coastline.
    What is the size (radius and area) of a circular island claiming a territorial waters of limit of 40km whose landmass is 75% of all territories claimed? Describe your method of finding a solution.

    Could someone please show me the working out?

    Answer: r=259km, area=210 026km^2
    Thanks
    Hello,

    let r be the radius of the island, then
    (r+40) is the radius of the complete territory:
    75% = (3/4) (for affirmation only )

    (3/4) * π * (r+40)ē = π * rē

    Expand the LHS and collect all terms on the LHS. You'll get:

    -(1/4)πrē + 60πr + 1200 = 0 . Divide by -(1/4)π

    rē - 240r - 4800 = 0.

    r ≈ 258.564 or r ≈ -18.564 The negative solution doesn't make much sense here.

    Area of the island: A(r) = π * rē that means: A(258.564) ≈ 210,032 kmē
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