Question

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

Answer 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

Answer 2

How can I get 38.8 as the answer

Answer 3

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

Answer 4

Solution of √3.h^3 - 64h^2 + 128h - 64 = 0
are h=0.87 , h=1.22 and h=34.9

Answer 5

I meant is 34.88 haha

Answer 6

typoo how did you get the sol'ns ?

Answer 7

u need to solve for h
√3h^3 - 64h^2 + 128h - 64 = 0

Answer 8

so @mayankdevnani is right.. @sauravshakya

Answer 9

I guess yes...

Answer 10

guess?? but answer is coorect

Answer 11

*correct

Answer 12

√3h^3 - 64h^2 + 128h - 64 = 0 how did you arrive to three answers ? quadratic eqn?

Answer 13

I see no error in the logic...

Answer 14

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

Answer 15

And since,
t=(4h / √3) / (h - 1)
h=0.87 is rejected because t cant be negative