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anonymous

  • one year ago

2700 of material is avaiblr to make a boc with a square base and a open top. determine the largesst volume of the box

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  1. anonymous
    • one year ago
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    @ganeshie8

  2. anonymous
    • one year ago
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    the open top thing is confusing me

  3. anonymous
    • one year ago
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    i am only missing 2700 cm2

  4. ganeshie8
    • one year ago
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    |dw:1433741377518:dw|

  5. ganeshie8
    • one year ago
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    surface area of box = (surface area of base) + (surface area of sides) = x^2 + 4xh we're given surface area equals 2700, so \[x^2+4xh=2700\tag{1}\]

  6. ganeshie8
    • one year ago
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    next, see if you can write an expression for the volume of box

  7. anonymous
    • one year ago
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    o yea i think the SA formula was confusing me how do u get it

  8. anonymous
    • one year ago
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    @ganeshie8 is the vloume=lwh

  9. ganeshie8
    • one year ago
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    for surface area, you just add up the areas of all the sides

  10. ganeshie8
    • one year ago
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    how many sides does that box have ?

  11. anonymous
    • one year ago
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    um 6

  12. ganeshie8
    • one year ago
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    careful, it has no top

  13. ganeshie8
    • one year ago
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    there is one base, which is a square and four lateral sides

  14. ganeshie8
    • one year ago
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    so in total it has 5 faces

  15. ganeshie8
    • one year ago
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    whats the area of base ?

  16. anonymous
    • one year ago
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    x2?

  17. ganeshie8
    • one year ago
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    Yes, area of base = \(x^2\)

  18. ganeshie8
    • one year ago
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    next notice that each lateral face has same dimensions : width = x height = h

  19. ganeshie8
    • one year ago
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    |dw:1433742821286:dw|

  20. ganeshie8
    • one year ago
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    what is the area of that lateral face ?

  21. anonymous
    • one year ago
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    um h * w

  22. ganeshie8
    • one year ago
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    w = x here right

  23. anonymous
    • one year ago
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    yes

  24. ganeshie8
    • one year ago
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    since the box has four lateral faces, the lateral area is simply \(4*xh\)

  25. ganeshie8
    • one year ago
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    so do you get how i arrived at the surface area equation \((1)\)

  26. anonymous
    • one year ago
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    oh ok yea

  27. ganeshie8
    • one year ago
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    the expression for volume would be \[V = x*x*h = x^2h\tag{2}\]

  28. ganeshie8
    • one year ago
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    solve \(h\) from first equation and plug it in abvoe

  29. anonymous
    • one year ago
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    so what does the open top do ?

  30. ganeshie8
    • one year ago
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    it does nothing, do you have "h" from first equation ?

  31. ganeshie8
    • one year ago
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    from first equation, \[x^2+4xh=2700\\~\\\implies 4xh=2700-x^2\\~\\\implies h = \frac{675}{x}-\frac{x}{4}\] yes ?

  32. anonymous
    • one year ago
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    h=V/x2

  33. anonymous
    • one year ago
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    okey yea i tryed it and my final answer is 135000 , what u get ?

  34. ganeshie8
    • one year ago
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    do you mean 13500 ? http://www.wolframalpha.com/input/?i=maximize+x*%282700-x%5E2%29%2F4%2Cx%3E0

  35. anonymous
    • one year ago
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    oh sorry yea

  36. anonymous
    • one year ago
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    so the open top is just for confusing ?

  37. anonymous
    • one year ago
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    i should ignore it the next time i see it ?

  38. ganeshie8
    • one year ago
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    what do you mean you should ignore it

  39. ganeshie8
    • one year ago
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    the surface area changes if it was not open top

  40. anonymous
    • one year ago
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    how would it look like then ?

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