## eroshea Group Title 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. one year ago one year ago

1. Shadowys Group Title

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

2. eroshea Group Title

wet portion = volume

3. Shadowys Group Title

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 Group Title

that's all..

5. Shadowys Group Title

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

6. eroshea Group Title

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

7. Shadowys Group Title

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 Group Title

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

9. Shadowys Group Title

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

10. eroshea Group Title

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

11. Chlorophyll Group Title

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 :/ )

12. Shadowys Group Title

So the area=volume? wow.