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Math Help - [SOLVED] Working out the volume of a cuboid

  1. #1
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    [SOLVED] Working out the volume of a cuboid

    Here is the information I've been given:

    The sum of the lengths of the 12 edges of a cuboid is xcm. The distance from one corner of the cuboid to the furthest corner is ycm. What is the total surface area of the cube in terms of x and y.

    This is what I've got so far:

    Call the three lengths on the cuboid a, b, c.

    The total surface area = 2ab+2ac+2bc
    As y is the longest diagonal, y^2=a^2+b^2+c^2
    And finally, as x is the total lengths, x=4a+4b+4c

    I've tried to re-arrange those equations to get the surface area in terms of x and y, but to no avail.

    All help appreciated,
    David



    EDIT: I've just realised that I've put this in the wrong sub-forum. Please could one of the moderators move this to the appropriate sub-forum?
    Last edited by dave1022; October 13th 2009 at 09:24 AM.
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  2. #2
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    Quote Originally Posted by dave1022 View Post
    Here is the information I've been given:

    The sum of the lengths of the 12 edges of a cuboid is xcm. The distance from one corner of the cuboid to the furthest corner is ycm. What is the total surface area of the cube in terms of x and y.

    This is what I've got so far:

    Call the three lengths on the cuboid a, b, c.

    The total surface area = 2ab+2ac+2bc
    As y is the longest diagonal, y^2=a^2+b^2+c^2
    And finally, as x is the total lengths, x=4a+4b+4c

    I've tried to re-arrange those equations to get the surface area in terms of x and y, but to no avail.

    All help appreciated,
    David



    EDIT: I've just realised that I've put this in the wrong sub-forum. Please could one of the moderators move this to the appropriate sub-forum?
    Hint
    (a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab+bc+ca)
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  3. #3
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    Oct 2009
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    Thanks for the hint!

    Now I've got:

    (x^2)/16=a^2+b^2+c^2+2(ab+bc+ca)

    Therefore:

    (x^2)/16=y^2+2(ab+bc+ca)

    Therefore:

    Surface area =((x^2)/16)-y^2

    Thanks for the hint
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