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Math Help - V and SA of rectangular Box

  1. #1
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    V and SA of rectangular Box

    Write an expression for the volume and surface are of a rectangular box if

    w=x+2
    l=2x+5
    h=x+4
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  2. #2
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    Quote Originally Posted by william View Post
    Write an expression for the volume and surface are of a rectangular box if

    w=x+2
    l=2x+5
    h=x+4
    V = lwh = ....

    S = 2(wl) + 2(hl) + 2(wh) = ..... (assuming the box is not open at the top)
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    V = lwh = ....

    S = 2(wl) + 2(hl) + 2(wh) = ..... (assuming the box is not open at the top)
    V=(2x+5)(x+2)(x+4) how would I simplify this?

    SA= 2(2x+5)(x+2)+2(2x+5)(x+4)+2(x+2)(x+4)
    =(4x+10)(x+2)+(4x+10)(x+4)+(2x+4)(x+4)
    =4x^2+4x^2+2x^2+8x+10x+16x+10x+8x+4x+20+40+16
    =10x^2+56x+76, correct?
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  4. #4
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    Quote Originally Posted by william View Post
    V=(2x+5)(x+2)(x+4) how would I simplify this? Mr F says: Why expand? It's fine like that.

    SA= 2(2x+5)(x+2)+2(2x+5)(x+4)+2(x+2)(x+4)
    =(4x+10)(x+2)+(4x+10)(x+4)+(2x+4)(x+4)
    =4x^2+4x^2+2x^2+8x+10x+16x+10x+8x+4x+20+40+16
    =10x^2+56x+76, correct?
    I substituted x = 1 and your SA gave the correct answer so it's probably OK (I don't check algebra that's this tedious - I always make mistakes from boredom).
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    Quote Originally Posted by mr fantastic View Post
    I substituted x = 1 and your SA gave the correct answer so it's probably OK (I don't check algebra that's this tedious - I always make mistakes from boredom).
    Alright, thanks.

    Do you have any input on how to get the expression for the volume.
    I am unsure how to expand and simplify (2x+5)(x+2)(x+4)
    I see you have written that it is unnecessary and i do take your word for it, although how would I if i wanted to?
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  6. #6
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    Quote Originally Posted by william View Post
    Alright, thanks.

    Do you have any input on how to get the expression for the volume.
    I am unsure how to expand and simplify (2x+5)(x+2)(x+4)
    I see you have written that it is unnecessary and i do take your word for it, although how would I if i wanted to?
    First expand (2x + 5)(x + 2): 2x^2 + 9x + 10.

    Now expand (2x^2 + 9x + 10)(x + 4).
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