Monty Hall

[JohnW2]

It almost sounds as if you are making the same mistake that I think ebee was making (and the mistake that Detlef probablythought I was making).

Which was what, exactly? I'm getting confused.

Assuming that BAS was asking (usuing your analogy) the equivalent of the volume of the earth, ignoring the fact that caves actually reduced its true volume.

If so, I wonder how you got the right answer so quickly. Maybe two errors which 'cancelled'? - firstly what you appear to be saying above and, secondly, assuming that the diameter of the sphere was the same as the length of the hole?

Has he actually said it is the right answer?

He hasn't, but I have The volume of the material left (hence the 'semantic' comments) after the drilling (i.e. with removed bit subtracted from volume of the original sphere) is numerically equal to what would be the volume of a sphere with a diameter equal to the length of the hole (which is less than the diameter of the original sphere).

I just assumed the volume of a sphere is the same regardless of the inside being solid or empty or part of each.

Semantics again, BAS was (we all assume) asking about the volume of the remaining material, not of the 'sphere shape'.

I suppose pedantically you could dispute the length of the drilling, hence the diameter, by measuring from the point of contact of the drill to first point of egress or the length of the sides of the empty cylinder after drilling but it is just a puzzle question.

That's not pedantic - it's the whole point of the maths, and the answer - as above the length of the hole is less than the diameter of the original sphere - andthat's why the answer is what it is.

Kind Regards, John

 

[ebee]

"I suppose pedantically you could dispute the length of the drilling, hence the diameter, by measuring from the point of contact of the drill to first point of egress or the length of the sides of the empty cylinder after drilling but it is just a puzzle question."

That was indeed what I was thinking - the point of the drill when touching then the movement of 10cm to drill thru would equal the diameter of the sphere.

Well that`s nearest I can come up with if we do not know the diameter of the drill.

Then it becomes is it total volume of the original sphere (does it just include the solid left or does it include the air in the hole?) If the new shape is considered to be a sphere bit with two flats (at hole break thru then it would not be a sphere now would it).

Oh dear, where is that BAS bloke when you need him?

 

[JohnW2]

"I suppose pedantically you could dispute the length of the drilling, hence the diameter, by measuring from the point of contact of the drill to first point of egress or the length of the sides of the empty cylinder after drilling but it is just a puzzle question."
That was indeed what I was thinking - the point of the drill when touching then the movement of 10cm to drill thru would equal the diameter of the sphere.

As I've just written to EFLI, that is the whole point of this 'puzzle'. The answer is what it is (and does not require knowlede of the diameter of the hole) because the length of the hole is less than the diameter of the sphere.

If you think about it, as the diameter of the hole gets larger, it's length decreases. Without doing the maths (unless one makes the iffy John Campbell assumption) you're not actually going to get an answer (or confirm that the answer does nt require knowledge of the diameter of the hole), but you should be able to see that the volume of the material that's left will be a function of the length of the hole (which itself is a function of the diameter of the hole.

Looking at the link posted by Detlef may well help you.

Kind Regards, John

 

[EFLImpudence]

Semantics again, BAS was (we all assume) asking about the volume of the remaining material, not of the 'sphere shape'.

NO. We did not all assume that. That is the whole point.
Bas said the volume of the original sphere remaining.

The volume of the Earth is not reduced because of the caves.



Also - there is a fundamental 'misprint' in the final line of text in Detlef's link.

 

[DetlefSchmitz]

Also - there is a fundamental 'misprint' in the final line of text in Detlef's link.

Go on...

 

[EFLImpudence]

No, I didn't read it all. sorry.

 

[ebee]

Hang on a min, I was assuming (oh silly me) that the drill had a point.

It could be a flat bottomed drill (ie a key-seater) therefore it would start drilling as soon as it hit the diameter but stop drilling before it hit the opposing point of the diameter because breakthu would occur which would be dependant upon the dia of the drill . Therefore our 10cm being the diameter of the sphere could be skewed either none, one or two drill diameter dependant radii.

Gosh

 

[riveralt]

Hang on a min, I was assuming (oh silly me) that the drill had a point.

It could be a flat bottomed drill (ie a key-seater) therefore it would start drilling as soon as it hit the diameter but stop drilling before it hit the opposing point of the diameter because breakthu would occur which would be dependant upon the dia of the drill . Therefore our 10cm being the diameter of the sphere could be skewed either none, one or two drill diameter dependant radii.

Didn't BAS say 'right through' and 'along an axis'?

 

[ebee]

"Didn't BAS say 'right through' and 'along an axis'?"

Well yes but I took "right through" to mean from start of meat removal to end of meat removal (ie no drilling in fresh air. and "along an axis" to mean thru the centre.

I could stand to be corrected though

 

[JohnW2]

Semantics again, BAS was (we all assume) asking about the volume of the remaining material, not of the 'sphere shape'.

NO. We did not all assume that. That is the whole point. Bas said the volume of the original sphere remaining.

Sorry - I should have said all of us other than ebee and you. I suppose it remains just possible that BAS is talking about a different problem/puzzle, but every manifestation I've seen of it makes it clear that what one is being asked about is the volume of material remaining in the object (which is no longer a sphere once it's been drilled). However, as I've said, if BAS actually meant what you think, then it become a matter of semantics, not the mathematical puzzle that the rest of us are talking about.

The volume of the Earth is not reduced because of the caves.

As above, if BAS was talking about the standard puzzle (with some semantic non-clarity), he would have been talking about the volume of material in the object - which is reduced by 'caves' (or drilled).

The fact remains that, as I've said, if (as you obvioulsy do) you believe that you were being asked to calculate the volume of the sphere (without subtraction of 'caves'), then, on that basis you got the answer wrong (because the diameter of the original sphere would be greater than 10cm - how much greater being dependent upon the diameter of the drilled hole)!

Kind Regards, John

 

[JohnW2]

"Didn't BAS say 'right through' and 'along an axis'?" ... Well yes but I took "right through" to mean from start of meat removal to end of meat removal (ie no drilling in fresh air. and "along an axis" to mean thru the centre.

That's all correct - but the crucial thing, and the 'trick' which catches many people, is that the 10cm he mentioned is the length of the (cylindrical) hole through the sphere, which will be less than the diameter of the sphere (increasingly less as the diameter of the hole increases).

Kind Regards, John

 

[ebee]

I think I see what you`re getting at John.

The length of the hole in the remaining metal of what was originally a true sphere is 10cm

But the diameter of the sphere to start with would vary from this 10cm figure by an amount dependant upon the diameter of the hole.

 

[ebee]

I think we were typing at the same time

 

[TonyW2]

O to 100% depending on the diameter of the drill and whether the hole is measured from the centre of a drill of no diameter or edge of the drill without consideration of the part sphere under the drill bit.
Well I know what I mean.
Think 10cm diameter drill on a 10cm diameter sphere.Then smaller to no diameter drill

 

[ebee]

Next week let`s have a go at "Schroedinger`s Cat" !