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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

  • 2 years ago
  • 2 years 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

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

    • 2 years 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

    • 2 years 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

    • 2 years ago
  5. Reyjuanx10 Group Title
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    I meant is 34.88 haha

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

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

    • 2 years ago
  8. Hares333 Group Title
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    so @mayankdevnani is right.. @sauravshakya

    • 2 years ago
  9. sauravshakya Group Title
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    I guess yes...

    • 2 years ago
  10. Hares333 Group Title
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    guess?? but answer is coorect

    • 2 years ago
  11. Hares333 Group Title
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    *correct

    • 2 years 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?

    • 2 years ago
  13. sauravshakya Group Title
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    I see no error in the logic...

    • 2 years 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

    • 2 years 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

    • 2 years ago
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