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Math Help - Least Surface Area Problem

  1. #1
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    Least Surface Area Problem

    Please see attachment.
    Attached Thumbnails Attached Thumbnails Least Surface Area Problem-geometry08.jpg  
    Last edited by WartonMorton; April 13th 2010 at 11:03 AM.
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  2. #2
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    Quote Originally Posted by WartonMorton View Post
    Please see attachment.
    I can't see any attachment
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  3. #3
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    Quote Originally Posted by earboth View Post
    I can't see any attachment
    Sorry about that. I think I figured out how to attach it now.
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  4. #4
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    Hi

    Let R be the radius of the cylinder and L its length

    The volume is V_0 = \pi R^2L + \frac43 \pi R^3 = 13.4 cm^3

    From this expression you can find L as a function of R

    The area is A(R,L) = 2\pi RL + 4 \pi R^2

    Substitute L function of R to get A(R)

    Calculate A'(R) to find the value of R which minimizes the area
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  5. #5
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    Quote Originally Posted by running-gag View Post
    Hi

    Let R be the radius of the cylinder and L its length

    The volume is V_0 = \pi R^2L + \frac43 \pi R^3 = 13.4 cm^3

    From this expression you can find L as a function of R

    The area is A(R,L) = 2\pi RL + 4 \pi R^2

    Substitute L function of R to get A(R)

    Calculate A'(R) to find the value of R which minimizes the area

    I got 1.845, how does this match up to what you got?
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  6. #6
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    I am getting 1.473 in
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  7. #7
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    Quote Originally Posted by running-gag View Post
    I am getting 1.473 in
    Any body else got 1.845 or 1.473?
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  8. #8
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    Quote Originally Posted by WartonMorton View Post
    Any body else got 1.845 or 1.473?
    The exact value of r is: r = \frac{\sqrt[3]{10050}}{10 \cdot \sqrt[3]{\pi}} \approx 1.473461286
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