Hi am stuck on this integration question:

The horizontal cross section of a bowl at a height h cm above its base is a regular hexagon of side x cm. Given that x²=16(h+1), find the volume of liquid in the bowl when its filled to a depth of 8cm.

the answer should be 960√3 cm³

Question

Hi  am stuck on this integration question:

The horizontal cross section of a bowl at a height h cm above its base is a regular hexagon of side x cm. Given that x²=16(h+1), find the volume of liquid in the bowl when its filled to a depth of 8cm.

the answer should be 960√3 cm³

anonymous · Answer

You should start by drawing a picture.

anonymous · Answer

ok i have got a bowl (looks like parabola) and a regular hexagon in the bowl is that correct?

anonymous · Answer

Bowls are usually circular.  It seems in this question the bowl is hexagonal.  The equation is telling use the length of the hexagon's sides with respect to height.

anonymous · Answer

So the first research you need to do is find the area of a hexagon with respect to its side.

anonymous · Answer

|dw:1356380563955:dw|

anonymous · Answer

this is one way of thinking about it...

anonymous · Answer

the area of the hexagon will be the six equilateral triangles knowing that we have height h and side x.
 w

anonymous · Answer

Also the angles of the hexagon are going to be equal, whatever they may be.

anonymous · Answer

|dw:1356380876433:dw|

anonymous · Answer

anyway, we need to find the area of this thing with respect to the side... got an idea?

anonymous · Answer

|dw:1356380981780:dw|