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Math Help - Volume Problem

  1. #1
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    Volume Problem

    How many jam tins can fit into this box if they have a diameter of 8cm and are 11cm high?

    I have worked out the volume of the box to be 21120\,\textrm{cm}^2 and the volume of the tin to be \pi \cdot 4^2 \cdot 11 = 552.92\,\textrm{cm}^2.
    When I divide the box by the cans, I get \frac{21120}{552.92} = 38.20 cans.
    But the answer should be 30 cans. What have I done wrong?
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  2. #2
    MHF Contributor
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    Hello Demonstration

    Welcome to Math Help Forum!
    Quote Originally Posted by Demonstration View Post
    How many jam tins can fit into this box if they have a diameter of 8cm and are 11cm high?

    I have worked out the volume of the box to be 21120\,\textrm{cm}^2 and the volume of the tin to be \pi \cdot 4^2 \cdot 11 = 552.92\,\textrm{cm}^2.
    When I divide the box by the cans, I get \frac{21120}{552.92} = 38.20 cans.
    But the answer should be 30 cans. What have I done wrong?
    You don't tell us what the dimensions of the box are. But have you taken into account the spaces in between the tins? If they are cylindrical (as I assume they are) then you can't pack them into the box without 'wasting' some space, can you?

    Grandad
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  3. #3
    Senior Member Educated's Avatar
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    Assuming the box is specially designed for packing tins:

    You must know that cylinderical things will not fit perfectly into square things.
    So, using the volume formula of a cylinder is useless. Instead, assume the tins aren't round, but like a block, rectangular block.

    Therefore:

    Volume = 8 \times 8 \times 11 = 704cm^3

    Now the volume of the box is 21120 cm^3 so...
    Last edited by Educated; August 30th 2010 at 09:48 PM.
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  4. #4
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    Hi, sorry, I was given a diagram and I forgot to mention the dimensions.

    The dimensions are 40\,\textrm{cm}\,\times 16\,\textrm{cm}\,\times 11\,\textrm{cm}.

    But what you're saying about wasted space makes perfect sense.

    So if I packed 5 in a row, with 2 rows, and 3 layers, that makes 30 cans.

    I get it now, thanks.
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