can you guys help me out of this?
An object in which the ends are regular hexagons was cut from a cylindrical wooden solid of length 24 inches and 1.3 inches in diameter. Find the volume of the said object with the least waste material that can be taken from the wood.

Question

can you guys help me out of this?
An object in which the ends are regular hexagons was cut from a cylindrical wooden solid of length 24 inches and 1.3 inches in diameter. Find the volume of the said object with the least waste material that can be taken from the wood.

anonymous · Answer

Do you know the height?

anonymous · Answer

there is no height given in the question.

anonymous · Answer

Do you mean that the length of the cylinder is 24in?

anonymous · Answer

Yes.

anonymous · Answer

well your apothem is .65 because it's half of your diameter. apothem=radius Here's a youtube video to help you solve this problem: http://www.youtube.com/watch?v=jeUZSRaSkis

anonymous · Answer

btw the answer is 26.35in^3 but I dont know the solution. I tried getting the side and solving for the volume but I only got 23.41in^3.

anonymous · Answer

Do you have a picture of the problem if so can you draw it out

anonymous · Answer

Sorry there's none.

hba · Answer

pi (1.3)^2 24/4=31.8 inch^3

anonymous · Answer

care to explain on how you get 24/4?

anonymous · Answer

Is this basically what needs to happen? You're cutting a hexagonal prism from a cylinder.

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anonymous · Answer

And then you want to figure out what the volume is? Then you just find out the area of the hexagon at the top, and multiply by the height of the cylinder.

anonymous · Answer

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The diameter of the circle is 1.3. So you've got 6 equilateral triangles with sides 1.3 / 2.

So the volume of the hexagonal prism should be 24 * 6 * (area of one of the triangles). (since the height is 24).

I'm getting that the area of one of those triangles is 1.3 / 2 * sqrt(3) / 2 * 1.3. (half base x height, where height is sqrt(3) / 2 * 1.3). But I might have made a mistake somewhere.

So I'm getting the volume of the hexagonal prism is 36 * (1.3)^2 * sqrt(3).

anonymous · Answer

I made mistakes in that thing above...

anonymous · Answer

In the thing above I made the sides of each of the 6 triangles as 1.3. But it should be 1.3/2. If you do that then I get that the volume is 6^2/4 * (1.3)^2 * sqrt(3) which comes out as 26.3444927831 which is what your thing says it should be.

I get that number from 24 * 6 * (area of one triangle). Because height is 24, there are 6 triangles at the top...

To get the area of one triangle, you have...
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So you can calculate the height, and then find the area of the triangle as half base * height, and then throw it all together to get the answer.