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Math Help - Maths Assignment Help !

  1. #1
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    Maths Assignment Help !

    Could someone please help me with this question, I really have know clue how to do this.

    A parcel is to be tied with a length of string in a normal way.

    Assume that the parcel is a cuboid with square cross section and with a volume (V) of 16000 cm^3. Find an expression for the length of string, L(x), in terms of the side of the square cross section, x

    And..

    determine the dimensions of the parcel that will minimize the length of string required.

    Any help would be greatly appreciated.
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  2. #2
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    Re: Maths Assignment Help !

    Quote Originally Posted by PapaJones View Post
    Could someone please help me with this question, I really have know clue how to do this.

    A parcel is to be tied with a length of string in a normal(?) way.

    Assume that the parcel is a cuboid with square cross section and with a volume (V) of 16000 cm^3. Find an expression for the length of string, L(x), in terms of the side of the square cross section, x

    And..

    determine the dimensions of the parcel that will minimize the length of string required.

    Any help would be greatly appreciated.
    1. Use V_{cuboid}= \text{base-area} \cdot \text{height}

    With your values: V = x^2 \cdot h~\implies~h=\frac{16000}{x^2}

    2. The length of the string consists of the circumferences of the cross-sections (I hope that this is meant by "the normal way" you mentioned). Two of the three cross-sections are equal due to the quadratic base area:

    L(x)= 4x + (2x+2h)+(2x+2h)=8x + \frac{4 \cdot 16000}{x^2}

    3. To minimize L differentiate L wrt x and solve L'(x) = 0 for x. You should come out with a cube.
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  3. #3
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    Re: Maths Assignment Help !

    Sorry, by "normal" I meant that the string goes all the way around the parcel including underneath it. Is the answer still the same?
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  4. #4
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    Re: Maths Assignment Help !

    Quote Originally Posted by PapaJones View Post
    Sorry, by "normal" I meant that the string goes all the way around the parcel including underneath it. Is the answer still the same?
    I've attached a sketch to show you what I believe is a normal way to tie up a parcel. (The red lines indicate the string)

    ... and I used this sketch to do my calculations.
    Attached Thumbnails Attached Thumbnails Maths Assignment Help !-paketschnur.png  
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  5. #5
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    Re: Maths Assignment Help !

    Thats correct for my question, except the string around the sides that doesn't go underneath the parcel. Only 2 strings in my question.
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  6. #6
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    Re: Maths Assignment Help !

    Quote Originally Posted by PapaJones View Post
    Thats correct for my question, except the string around the sides that doesn't go underneath the parcel. Only 2 strings in my question.
    then modify what earboth has provided as a solution path ... you should be able to come up with a suitable equation on your own to minimize.
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