Volume, Weight - Hexagonal Steel Rod

[Guest]

A hexagonal steel rod is 3/4" on a side and 10' in length. Determine volume and weight of the rod.

Steel weighs .283 lbs. per cu. in.

Check my calculations:

Area = .2598 * s^2

.2598 * .75 * .75 = 0.146 * 120 = 17.52 = 18 cu. in.

18 * .283 = 5.094 lbs.

I am not sure.

Also, I found another formula:


Area = 1/2 * perimeter * apothem.

I don't know what the apothem is.

[Guest]

Deal with the problem logically
Find the area of the end then multiply by the length
then multiply by weight per cu. in

[Guest]

Area - .2598 * s^2

A hexagon has 6 sides.

.2598 * 6 * 6 *.75 = 7.0146 * 120 = 841.752 cu. in.

841.752 *.283 = 238.21 = 238 lbs.

I am not sure.

[Guest]

Deal with the problem logically
Find the area of the end then multiply by the length
then multiply by weight per cu. in

Where are you getting your numbers from?
Did you draw a diagram to see waht a hexagon looks like?
Explain what you are doing rather than just writing random numbers.

[Guest]

"Where are you getting your numbers from? Area formula
Did you draw a diagram to see waht a hexagon looks like? Yes
Explain what you are doing rather than just writing random numbers"

2598(?) * 6(side) * 6(side) *.75 (on a side) = 7.0146 * 120 (length) = 841.752 cu. in.

841.752 *.283 (cu. in of steel) = 238.21 = 238 lbs.

I am still not sure.

[Guest]

"Where are you getting your numbers from? Area formula.....What formula are you using
Did you draw a diagram to see waht a hexagon looks like? Yes......Then what does it look like.....
Explain what you are doing rather than just writing random numbers" The numbers you are using are just random?????

2598(?) * 6(side) * 6(side) *.75 (on a side) = 7.0146 * 120 (length) = 841.752 cu. in.

841.752 *.283 (cu. in of steel) = 238.21 = 238 lbs.

What does all this mean??????

[Guest]

Formula - .2598 * s^2 - I don't know what the .2598 is.

A hexagon has 6 sides - similar to a "stop" sign - 2 less sides.

I used numbers from the problem - 3/4" on a side, 10' length (I changed the feet to inches for length).

I tried to find the area of the end then multiplied by length, then multiplied by weight of cu. in.

.2598 * 6 * 6 * .75 = 7.0146 (area of end)

7.0146 * 120 = 841.752 cu. in. (volume of rod)

841.752 * .283(lbs. of steel per cu. in.) = 238.21 = 238 lbs. (weight of rod)

[Guest]

We will carry out some stepwise refinement.....
Formula - .2598 * s^2 - I don't know what the .2598 is..

2598 * 6 * 6 * .75 = 7.0146 (area of end)

You looked at a hexagon and you see 6 sides.....
It also looks roughly circular....round circle with bits of the curve cut off to leave 6 straight edges
If it is circular then it has a centre.....
Two adjacent edges join to a point......there are 6 points
If you join opposite points or corners you find they all cross at the centre.
Tha space between the lines look like triangles.....there are 6 of them....around the circle.
They are all the same size.....so they have all the same angles
The angles at the centre will be 360 divided by 6 = 60 degrees
All the lines from the centre out to the edge will be the same length.
So all the triangles will have at least 2 sides the same length with the angle between them = 60 degrees.
A triangle that ha 2 sides equal is an isosoles triangle and also has 2 angles equal
So the 2 equal angles are 180 - 60 = 120 divided by 2 = 60.
So that means all the angles are equal to 60 degrees.
A triangle with all 3 angles equal is an equilateral triangle and also has all side equal.
So the sides of the hexagon must be the same length as the distance from the centre to the outer edge points.
So we have 6 equal triangles, If we can find the area of 1 we can multiply by 6.

A general formula for the area of any triangle is 0.5 x A x B x Sin(angle between them) where A and B is the length of the 2 adjacent sides. and multiply by 6 to get all of them.
So in terms of the hexagon of side length "s" in your question.......A and B are both equal to "s"

Area of hexagon = 6 x 0.5 x (s^2) x Sin60degrees.

Sin 60 = 0.866
0.5 x 6 = 3
3 x 0.866 = 2.598

So Area of hexagon A = 2.598 * S^2

Whis is your starting formula which you seem to have written down many times incorrectly

......Work through the question logically.............

[Guest]

I know what you are saying but I don't understand.

[Guest]

We have now established the area formula of a hexagon so all you have to do is use it.

Find the area of the hexagon end then multiply by the length converted to inches
then multiply by weight in lbs per cu. in

[Guest]

2.598 * .75 *.75 = 1.461375 ( area of end)

1.461375 * 120 = 175.365 cu. in. (volume)

175.365 * .283 = 49.628 = 50 lbs.

If that is not correct, I don't know.

[Guest]

Yes, that's it.......
Isn't it simple when you work logically through it.............

[Guest]

Yes it is and easier. Thanks again.