Maths help (making a cuboid)!

Ahleckz

Ahleckz

Ahleckz

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My friend has given me the following question. I have no idea why he has asked me, but meh. I provided an answer but we're not sure if it's the best way.

I have a square sheet of acrylic measuring 1200x600x4 (mm).

I want to turn this into a cuboid. I require the dimensions of 5 panels in the most efficient manner possible.

Can anyone assist?

I suggested dividing the square into 6, then cut 4 sixths of that out to make the four sides (shaving 4mm off two panels so they fit together) and then using the left over as the base.
 
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So you have 2.9760 m^2
Divided by 6 =0.496m^2
Then square root is 0.7m
So you want length and height 0.7m I think.
This is Tuesday night, so bleh it might be wrong technique.
 
efficient as in biggest box possible?

if I remember back to GCSE days, you'll have to use differentiation... should be plenty of solutions online.
 
before i get into the maths, can you confirm a couple of my assumptions/questions please?
i'm assuming that you:
- cant cut the acrillic into more than 6 pieces and then glue the pieces back together. if that were the case you could make the acrylic into dust and then make a perfect cube
(or infinitly close to a cube while not being a cube, to satisfy the whole cuboid part of the question)
- are we leaving this as an open top cuboid or a completely closed cuboid (5 or 6 faces from the acrylic)
- do the sheets of acryllic have to be joined properly (all 4mm of its depth touching another side), or can we just make the edges touch to satisfy a join
 
We can't turn it into dust.
It's a box, not a cuboid. I said the wrong thing. Thus 5 sides.
Yeah, it needs to be sealed totally. Imagine it has to be watertight.

Cheers Reaper!
 
RomanNose said:
So you have 2.9760 m^2
Divided by 6 =0.496m^2
Then square root is 0.7m
So you want length and height 0.7m I think.
This is Tuesday night, so bleh it might be wrong technique.
Click to expand...

Right idea, wrong numbers.
He has 0.72 square meters of acrylic.
you want 34cm squares of acrylic for the least wastage. (or 37cm for only 5 sides). Too bad you can't cut pieces that size however.

I think 30cm squares are the biggest that can be cut in one piece actually, since one side is 60cm long.
 
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What's the box for then, any idea at all?

Hard to give advice without knowing, as depending on how its done you will lose dimention through swarf / cutting. Unless you hook up the laser that is!
 
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OK, I've now been given more information, which should have been given at the beginning. He wants to make this:

WxXOc.jpg


That has the dimensions of (in inches)
12x12 Base
12x20 Front/rear
11.5x20 sides (using 1/4" glass hence the .5)
He wants to make the same thing with 1200x600x4 (mm) acrylic.

He wants to keep the aspect ratio.
 
Ahleckz said:
OK, I've now been given more information, which should have been given at the beginning. He wants to make this

That has the dimensions of (in inches)
12x12 Base
12x20 Front/rear
11.5x20 sides (using 1/4" glass hence the .5)
He wants to make the same thing with 1200x600x4 (mm) acrylic.

He wants to keep the aspect ratio.
Click to expand...

Alright let's do this.

Since the base is square, and the height is 20/12 times the length of the base, then if we call base length l, height = 5l/3.

Surface area of the tank is;

A = l^2 + 4(l*5l/3)
= (23/3)l^2

so when l = 300mm, A = 6.9*10^5 mm^2

The area of our acrylic sheet is 1200x600 = 7.2*10^5 mm^2.

Using the above formula, when A = 7.2*10^5, l = 306 mm (rounded down to nearest mm)

Times that by 5/3 to get out height and we have 511mm

So the dimensions of your acrylic tank should be;
Base - 306x306
Front/Rear - 306x511
Sides - 302x511

Giving you a total usage of 7.15*10^5 mm^2 usage of your sheet.

All of that is irrelevant however, as it's impossible to make those cuts using one sheet.

So, we need to work out the maximum size cut we can make so that we only have to use one sheet. The most efficient way to cut the sheet would be to make the 4 long cuts in the same orientation of the longer side of the sheet, then make the 5th and final base cut with the remainder of the sheet.

Given that the longer cuts are 5/3 the length of the base, then the amount of length, l, we have down the sheet is (13/3)l. So, 1200 / (13/3) = 276mm. So the biggest we can cut the base is 276mm. Which gives a height of (5/3)*276 = 460mm

So new dimensions are;

Base - 276x276
Front/Rear - 276x460
Sides - 272x460

This gives a total usage of 5.8*10^5 mm^2. Out of the total sheet, that gives you 19.4% wastage.
 
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