## eroshea 3 years ago A flower vase, in the form of a hexagonal prism, is to be filled with 512 cubic inches of water. Find the height of the water if the wet portion of the flower vase and its volume are numerically equal.

Is the wet portion a ratio? or does it simple mean wet portion= volume?

2. eroshea

wet portion = volume

Is there any more numbers? The volume of a hexagonal prism is $$V=\frac{\sqrt 3}{4}r^2 H$$ where r is the side of the hexagon.

4. eroshea

that's all..

Hmmm....strange question this one. Well, it might mean that H=r.

6. eroshea

the answer was 34.88 inches but i want to know how to get it..

Either I misunderstood the question or it lacks something. Sorry, Idk why it is 34.88. Though I can show how to calc the volume of the prism|dw:1352974254691:dw| As such the volume is area of six triangles x height. $$V=(6)(\frac{1}{2} r^2 sin 60)(h)$$ $$V=(\frac{3 \sqrt 3}{4} r^2)(h)$$

8. eroshea

ok.. thank you.. i'll try answering it again

You're welcome :) sorry I can't be of more help.

10. eroshea

that's fine.. thanks for the help :))

11. Chlorophyll

V = SA = 512 V = ( 3 √3 /2 ) a² * H 512 = 2.6 a² * H ->H = 197.1 / a² SA = 2.6 a² + 6a h 512 = 2.6 a² + 6a ( 197.1 / a²) = 2.6 a² + 1,182.6 / a 512a = 2.6a³ + 1,182.6 ( plug into your calculator to solve it :/ )