Maths puzzle four

[EddieM]

WARNING: This one is a shocker.

This was posted on the forum a while ago, I don't think it got a mathematical answer, unsurprisingly.

ok,

You have a cube of wood (it's actually irrelevant what it's made of) measuring 10cm x 10 cm x 10 cm.

you drill a perfect 1 cm hole all the way through between top and bottom vertices of the cube.

What percentage of the material is left?

Ow!

 

[Iamchamps]

99%

 

[EddieM]

99%

I'm sorry, That's likely incorrect, anyway you have to show your workings.

 

[Iamchamps]

Break them down into layers 10 x 10 is 100 you drill top to bottom so take 1 off each layer which leaves 99. In effect 1% from each layer makes 99% of the whole cube.

 

[Bodd]

90%

 

[EddieM]

Break them down into layers 10 x 10 is 100 you drill top to bottom so take 1 off each layer which leaves 99. In effect 1% from each layer makes 99% of the whole cube.

Well no, cos across the vertices in 2D is sqrt 10^2 × 10^2 and that's just in 2D. This drill bit is going across opposing vertices in 3D.

 

[Iamchamps]

Do you know the answer or just telling me I’m incorrect? From the question I believe my answer to be correct.

 

[EddieM]

Do you know the answer or just telling me I’m incorrect? From the question I believe my answer to be correct.

No I don't, I believe it is a very complex mathematical problem. With all respect I'm not sure you have understood the problem fully, however you could be correct.

So to try to rationalise.

A 10x 10x 10 cm3 cube would be 1000 cm3

A 1cm perfect hole drilled from 2 opposing faces would be

3.1415926 x 1^2 x 10 = 31.42

So the amount of material removed in that very simple example would be 31.42 / 1000 = 3.142%

 

[EFLImpudence]

3.1415926 x 1^2 x 10 = 31.42

That should be
3.1415926 x 0.5^2 x 10 = 7.854

 

[EddieM]

That should be
3.1415926 x 0.5^2 x 10 = 7.854

Ah yes, true, sorry used d instead of r.

 

[EddieM]

Problem still stands.

 

[tony1851]

When you say vertices, do you mean this?

 

[EFLImpudence]

I think the answer is approximately 98.68%.

Vortex to vortex is the hypotenuse of a rectangle triangle 10 x 14.14 (sq.rt 200) which is 17.32 (sq.rt. 300).

Not sure how to calculate the corners until the drill is all in so just knocked off 0.5cm.

so 0.5² x Pi x 16.82 = 13.2 cu.cm. so 986.8 cu.cm. remaining = 98.68%

 

[Bodd]

I correct myself.

96%

 

[EddieM]

the devil is in the corners, which is very complicated.