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Math Help - [SOLVED] Help designing tank

  1. #1
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    [SOLVED] Help designing tank

    The problem is: You have to design a 500ft^3 square-based, open-top, rectangular holding tank. It is to be made from stainless steel plates. Find the dimensions for the base and height that will make the tank weigh as little as possible.

    I know that you take 500=h*x^2 and find that h=500/(x^2). Then I think you're supposed to plug it into the SA equation and get SA=(x^2)+4x[500/(x^2)], but I'm not sure and I keep on getting impossible answers after that.
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  2. #2
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    Hi there smartartbug, happy new year!

    I agree that SA = x^2+4xh = x^2+2000x^{-1} after substitution

    now \frac{dSA}{dx}= 2x-\frac{2000}{x^2}

    Now set \frac{dSA}{dx}=0 and solve


    Spoiler:

    0=2x-\frac{2000}{x^2}

    \frac{2000}{x^2}=2x

    1000=x^3

    x=10
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  3. #3
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    Thumbs up

    Thank you so much! I totally missed that subtract 1 on the -1. So now I'm getting x=10 and h=5. I hope I did that last part right. Thanks again!
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  4. #4
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    Quote Originally Posted by smartartbug View Post
    So now I'm getting x=10 and h=5. I hope I did that last part right.





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