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anonymous
 4 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
anonymous
 4 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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mayankdevnani
 4 years ago
Best ResponseYou've already chosen the best response.1It 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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0How can I get 38.8 as the answer

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0But none of the solution of √3.h^3  64h^2 + 128h  64 = 0 is h=38.8

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Solution of √3.h^3  64h^2 + 128h  64 = 0 are h=0.87 , h=1.22 and h=34.9

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I meant is 34.88 haha

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0typoo how did you get the sol'ns ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0u need to solve for h √3h^3  64h^2 + 128h  64 = 0

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so @mayankdevnani is right.. @sauravshakya

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0guess?? but answer is coorect

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0√3h^3  64h^2 + 128h  64 = 0 how did you arrive to three answers ? quadratic eqn?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I see no error in the logic...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=%E2%88%9A3*x%5E3++64x%5E2+%2B+128x++64+%3D+0

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0And since, t=(4h / √3) / (h  1) h=0.87 is rejected because t cant be negative
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