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Reyjuanx10 Group Title

A flower vase in the form of a hexagonal prism , is to be filled with 512 cubic in of water . Find the height of the water if the wet portion of the flower vase and its volume area numerically equal

  • one year ago
  • one year ago

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  1. mayankdevnani Group Title
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    It is a hexagonal prism, and I presume a regular hexagon. The "wet portion" of the prism is the base and the inner sides (not the lid nor anywhere on the outside) Let the sides of the hexagon be length t, and its height be h The area of the hexagon is A = (3√3 / 2) * t^2 The volume of the prism is therefore hA = h(3√3 / 2) * t^2 The perimeter around the prism is equal to 6t The area of the "wet portion" is therefore 6th + (3√3 / 2) * t^2 We require the volume to equal this area, thus h(3√3 / 2) * t^2 = 6th + (3√3 / 2) * t^2 Divide through by t(3√3 / 2) to get h * t = (2 / 3√3) * 6h + t (4h / √3) + t - ht = 0 = (4h / √3) + t(1 - h) (4h / √3) = -t(1 - h) (4h / √3) = t(h - 1) (4h / √3) / (h - 1) = t We know the volume is 512, so hA = h(3√3 / 2) * t^2 = 512 h(3√3 / 2) * ((4h / √3) / (h - 1))^2 = 512 h(3√3 / 2) * (4h / √3)^2 / (h - 1)^2 = 512 h(3√3 / 2) * (16h^2 / 3) / (h^2 - 2h + 1) = 512 h(√3) * (8h^2) / (h^2 - 2h + 1) = 512 √3.8h^3 = 512 (h^2 - 2h + 1) √3.8h^3 - 512h^2 + 1024h - 512 = 0 √3.h^3 - 64h^2 + 128h - 64 = 0 http://ph.answers.yahoo.com/question/index?qid=20100505051316AAXv8po

    • one year ago
  2. Reyjuanx10 Group Title
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    How can I get 38.8 as the answer

    • one year ago
  3. sauravshakya Group Title
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    But none of the solution of √3.h^3 - 64h^2 + 128h - 64 = 0 is h=38.8

    • one year ago
  4. sauravshakya Group Title
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    Solution of √3.h^3 - 64h^2 + 128h - 64 = 0 are h=0.87 , h=1.22 and h=34.9

    • one year ago
  5. Reyjuanx10 Group Title
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    I meant is 34.88 haha

    • one year ago
  6. Reyjuanx10 Group Title
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    typoo how did you get the sol'ns ?

    • one year ago
  7. sauravshakya Group Title
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    u need to solve for h √3h^3 - 64h^2 + 128h - 64 = 0

    • one year ago
  8. Hares333 Group Title
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    so @mayankdevnani is right.. @sauravshakya

    • one year ago
  9. sauravshakya Group Title
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    I guess yes...

    • one year ago
  10. Hares333 Group Title
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    guess?? but answer is coorect

    • one year ago
  11. Hares333 Group Title
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    *correct

    • one year ago
  12. Reyjuanx10 Group Title
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    √3h^3 - 64h^2 + 128h - 64 = 0 how did you arrive to three answers ? quadratic eqn?

    • one year ago
  13. sauravshakya Group Title
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    I see no error in the logic...

    • one year ago
  14. sauravshakya Group Title
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    http://www.wolframalpha.com/input/?i=%E2%88%9A3*x%5E3+-+64x%5E2+%2B+128x+-+64+%3D+0

    • one year ago
  15. sauravshakya Group Title
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    And since, t=(4h / √3) / (h - 1) h=0.87 is rejected because t cant be negative

    • one year ago
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