Here's a maths one for ya

[big-all]

maybe we are talking cross purposes i am talking about the shape off the removed bit as having a point assuming it comes out as a solid rather than dust

 

[calorific]

Must admit, the use of a core drill was not considered

 

[OwainDIYer]

the wood removed at the corner will be a triangular pyramid with a circular base. Don't know what that's called or how its volume is calculated.

 

[calorific]

the wood removed at the corner will be a triangular pyramid with a circular base. Don't know what that's called or how its volume is calculated.

If it is that solid then I can see a way of calculating that by adding together ("integrating") an infinite number of segments whose areas are easily determined in general form, and subtracting thrice the result from what would have been an enveloping cone.

Just want to be sure that it's that shape though

 

[chapeau]

the wood removed at the corner will be a triangular pyramid with a circular base. Don't know what that's called or how its volume is calculated.

Well the volume of any 'regular' pyramid is 1/3 x area of base x height. This comes from integrating (therefore adding) the slices of the known area of the base to the point (which has zero area) over the height. But I don't think the base is circular.

There are four pyramids at each 'corner', the base has two straight sides and one circular side where the drill bit has passed by. So that's the crucial thing to realise, 1/3 x base x height applies to that volume, the rest is geometry.

 

[calorific]

the rest is geometry.

You were going well until you said that

You gotta admit, it's an intriguing little puzzle/problem though.

 

[joe-90]

The base must be circular (think core bit).

 

[calorific]

Well the volume of any 'regular' pyramid is 1/3 x area of base x height. This comes from integrating (therefore adding) the slices of the known area of the base to the point (which has zero area) over the height.

How do you integrate squares, or trapezoids if you want to be a little more accurate, to build up a square based pyramid? Can;t see what function you'd be integrating

 

[calorific]

The base must be circular (think core bit).

And yet the faces are flat

 

[joe-90]

It's a mystery, that's for sure.

 

[EddieM]

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.

whilst pondering the answer i will just say, what a load of toss joe.

 

[chapeau]

Well the volume of any 'regular' pyramid is 1/3 x area of base x height. This comes from integrating (therefore adding) the slices of the known area of the base to the point (which has zero area) over the height.

How do you integrate squares, or trapezoids if you want to be a little more accurate, to build up a square based pyramid? Can;t see what function you'd be integrating

See post below...

Easier with pictures

Bloody edit....

 

[JBR]

Why bother with maths - it's too difficult, at least for me!

Drill out the cube (or cuboid) then immerse in water to measure the amount of water displaced, and that will give you the remaining volume.

If I recall correctly, one litre = 1000cc.

 

[EddieM]

10x10x10 = 1000 cubic cm.

the drill driven down diagonally will remove. 40.771 cubic cm.

leaving 959.229 cubic cm.


eww, thats all wrong, back to the drawing board, my son !!

 

[chapeau]

Need workings.

For calorific, here is the calculus with all the squiggly stuff.

Wiki

http://en.wikipedia.org/wiki/Pyramid_(geometry)#Volume

Dummies

http://www.dummies.com/how-to/content/measuring-the-volume-of-a-pyramid.html