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    A box with a volume of 600cm^3 (5cm deep, 10cm length and 12cm width) has a inner cavity of volume 300cm^3. the thickness of the container walls and of the base is x cm.

    (a) the box is 5cm deep write down, in terms of x, an expression for the depth of the inner cavity.

    (b) Obtain, in terms of x, an expression for the volume of the inner cavity.

    Can anyone help?

    Thanks,

    Dan
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    Its not easy if you cant do it?

    Write out all the things you know...transpose the formulae and see what you get in terms of the varibles.
    Plug them back in where required
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    (a) is 5-x

    but its (b) that is getting me!

    (5-x)(10-x)(12-x) is what i think it is.

    ???
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    (Original post by dantheram)
    (a) is 5-x

    but its (b) that is getting me!

    (5-x)(10-x)(12-x) is what i think it is.

    ???
    If I interpret your q correctly a quick sketch would show

    (5-x)(10-2x)(12-2x) = 300
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    (Original post by gdunne42)
    If I interpret your q correctly a quick sketch would show

    (5-x)(10-2x)(12-2x) = 300
    where does the 2x come from?
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    how do we know that the cavity has a length and width that are minus twice the depth?
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    (Original post by dantheram)
    how do we know that the cavity has a length and width that are minus twice the depth?
    Since you know the thickness of the wall is 'x', you have to subtract it twice to get the length and width of the inner cavity since the walls on BOTH sides of the inner cavity are x thick.

    For example, and disregard the bad drawing, if that picture below was the box, the | would represent the outer walls of the box, and the ! would represent the boundary of the inner cavity.

    | ! ! |
    | ! ! |

    In that drawing, thickness of the walls (| - !) has to be subtracted twice because the walls on each side are (| - !) thick.
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    (Original post by pokerplayer1191)
    Since you know the thickness of the wall is 'x', you have to subtract it twice to get the length and width of the inner cavity since the walls on BOTH sides of the inner cavity are x thick.

    For example, and disregard the bad drawing, if that picture below was the box, the | would represent the outer walls of the box, and the ! would represent the boundary of the inner cavity.

    | ! ! |
    | ! ! |

    In that drawing, thickness of the walls (| - !) has to be subtracted twice because the walls on each side are (| - !) thick.
    thank you,

    dan
 
 
 
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