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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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

Mathematics
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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
How can I get 38.8 as the answer
But none of the solution of √3.h^3 - 64h^2 + 128h - 64 = 0 is h=38.8

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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
I meant is 34.88 haha
typoo how did you get the sol'ns ?
u need to solve for h √3h^3 - 64h^2 + 128h - 64 = 0
I guess yes...
guess?? but answer is coorect
*correct
√3h^3 - 64h^2 + 128h - 64 = 0 how did you arrive to three answers ? quadratic eqn?
I see no error in the logic...
http://www.wolframalpha.com/input/?i=%E2%88%9A3*x%5E3+-+64x%5E2+%2B+128x+-+64+%3D+0
And since, t=(4h / √3) / (h - 1) h=0.87 is rejected because t cant be negative

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