Here's a maths one for ya

[calorific]

Imagine you have a 10cm by 10cm by 10cm wooden cube, and you want to drill out the longest hole possible using a 1cm radius drillbit. What is the volume of the wood that is left?

Hope you spot the slight problem with trying to do this calculation. Damned if we can work it out!!!

 

[chapeau]

Probably going to need some integral calculus. Any structural engineer worth his salt should be able to do this sort of thing in his sleep.

 

[OwainDIYer]

The longest hole will be a diagonal.

The diagonal of a cube Sqrt(3)*L which is is 17.321 cm

The volume of wood removed will be a cylinder 17.321 long x 1 cm radius.

Volume of the cylinder is 54.4 cm3.

Therefore the volume of wood left is (10x10x10) 1000 cm3 less 54.4 cm3 which is 945.6 cm3.

This does not take into account the fact that the wood removed isn't a perfect cylinder as it's drilling to/out of the pointy part of the corner of the cube rather than flat surfaces.

 

[big-all]

the diagonal is about 14ch about 165 mm from opposite
1cm radius is 2cm accross so the first and last 1cm ish is a triangle so around 35% full capacity
so about 14.5cmx pir square 3.152?? 145x 3.152=457 2x1/3=2/3[the points each end] = 2.11so around 460mm or 46cm

 

[calorific]

This does not take into account the fact that the wood removed isn't a perfect cylinder as it's drilling to/out of the pointy part of the corner of the cube rather than flat surfaces.

Aye. That's the bit we're struggling with.

Not even entirely sure what sort of shape has been drilled off before the normal cylinder is drilled out. Even more entertaining is the thought of the original block being a cuboid, so whatever the corner piece is ain't even symmetrical

 

[calorific]

Probably going to need some integral calculus. Any structural engineer worth his salt should be able to do this sort of thing in his sleep.

So far it's flummoxed 5 maths graduates, an MSc in maths and three science teachers with PhD's!

 

[big-all]

you have a tube with a 3sided triangle with identical faces at each end

 

[joe-90]

It's not possible to estimate as you are putting a round peg into a square hole so to speak, and since Pi can't be calculated without incurring infinity it can't be done on paper.

Only way to do it is to weigh it before drilling and after, but you'd never get the same answer twice, thus chaos theory is invoked.

 

[chapeau]

Probably going to need some integral calculus. Any structural engineer worth his salt should be able to do this sort of thing in his sleep.

So far it's flummoxed 5 maths graduates, an MSc in maths and three science teachers with PhD's!

None of whom are Structural Engineers worth their salt. These lads have to work out masses of strange shapes and that means calculating volumes.

Though probably most estimate in the real world.

 

[calorific]

you have a tube with a 3sided triangle with identical faces at each end

Are you sure the end faced are triangular and not curved? More to the point, even though working out how much cylinder is removed has it's own difficulties, it's working out what actual shape has gone before you get to that point - is it a circular based pyramid??

It's not possible to estimate as you are putting a round peg into a square hole so to speak, and since Pi can't be calculated without incurring infinity it can't be done on paper.

It's OK, feel free to leave it in terms of PI if you like

Only way to do it is to weigh it before drilling and after, but you'd never get the same answer twice, thus chaos theory is invoked.

Nice try joe, but try answering the blo*dy question

 

[calorific]

None of whom are Structural Engineers worth their salt. These lads have to work out masses of strange shapes and that means calculating volumes.

Anyone know any on here?

Though probably most estimate in the real world.

This ain't a real life question though

 

[big-all]

am i the only one thats noticed its radius so double for the hole size

 

[calorific]

am i the only one thats noticed its radius so double for the hole size

Owain spotted it in his calculation of PI*r^2.

I suspect that you've got a drill-press, so if you get a few spare minutes over the next few days and an offcut, any chance of using it to try it out and post a few piccies?

 

[big-all]

your 3 sided triangles will have a curve as one edge

 

[calorific]

your 3 sided triangles will have a curve as one edge

Ignoring the camber of the drill bit, are you sure about this since until you get a full width of drill going on, the edges of the drill bit will be in air, if you catch my meaning