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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
 one year ago
 one year 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
 one year ago
 one year ago

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mayankdevnaniBest ResponseYou've already chosen the best response.1
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

Reyjuanx10Best ResponseYou've already chosen the best response.0
How can I get 38.8 as the answer
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
But none of the solution of √3.h^3  64h^2 + 128h  64 = 0 is h=38.8
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
Solution of √3.h^3  64h^2 + 128h  64 = 0 are h=0.87 , h=1.22 and h=34.9
 one year ago

Reyjuanx10Best ResponseYou've already chosen the best response.0
I meant is 34.88 haha
 one year ago

Reyjuanx10Best ResponseYou've already chosen the best response.0
typoo how did you get the sol'ns ?
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
u need to solve for h √3h^3  64h^2 + 128h  64 = 0
 one year ago

Hares333Best ResponseYou've already chosen the best response.0
so @mayankdevnani is right.. @sauravshakya
 one year ago

Hares333Best ResponseYou've already chosen the best response.0
guess?? but answer is coorect
 one year ago

Reyjuanx10Best ResponseYou've already chosen the best response.0
√3h^3  64h^2 + 128h  64 = 0 how did you arrive to three answers ? quadratic eqn?
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
I see no error in the logic...
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.1
http://www.wolframalpha.com/input/?i=%E2%88%9A3*x%5E3++64x%5E2+%2B+128x++64+%3D+0
 one year ago

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