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Reyjuanx10

  • 2 years ago

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

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  1. mayankdevnani
    • 2 years ago
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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. Reyjuanx10
    • 2 years ago
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    How can I get 38.8 as the answer

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

  4. sauravshakya
    • 2 years ago
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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

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

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

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

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

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

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

  11. Hares333
    • 2 years ago
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    *correct

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

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

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

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

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