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Math Help - Another Math WordProblem

  1. #1
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    Another Math WordProblem

    Stewart Cannery will package tomato juice in a 2L(2000 cubic centimeters) cylindrical can. Find the radius and height if the can is to have a surface area that is less than 1000 square centimeters.
    (Hint: Use a rational Inequality on your calculator)
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  2. #2
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    Consider the following equations

    \displaystyle 2000= \pi r^2h

    and

    \displaystyle 2\pi r (r+h)<1000
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  3. #3
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    How to find height and radius now?
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  4. #4
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    Quote Originally Posted by thelensboss View Post
    How to find height and radius now?
    h = \dfrac{2000}{\pi r^2}

    sub this expression for h in the inequality provided by pickslides ... solve for r
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  5. #5
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    I got 2(pi)(r^3)< (1000(r-4))???
    Please help
    tell me how to get the answer using the graphing calculator plesae thanks
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  6. #6
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    Quote Originally Posted by thelensboss View Post
    I got 2(pi)(r^3)< (1000(r-4))???
    Please help
    tell me how to get the answer using the graphing calculator plesae thanks
    2\pi r(r+h) < 1000

    2\pi r \left(r + \dfrac{2000}{\pi r^2}\right) < 1000

    2\pi r^2 + \dfrac{4000}{r} < 1000

    0 < 1000 - 2\pi r^2 - \dfrac{4000}{r}

    0 < 500 - \pi r^2 - \dfrac{2000}{r}

    graph the right side of the inequality using x to represent r ... look for where the graph is greater than 0 (i.e. above the x-axis) ... you'll have a range of choices for r. once you pick a value for r, calculate the corresponding value for h that yields the fixed volume.
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