Monty Hall

[JohnW2]

What is the volume of a 10cm diameter sphere?

(500/3)π cu cm, which is about 523.6 cu cm

Only "about" ?

Well, yes. 523.598775598298 is a bit closer - but still only 'about'!

And, as asked, when the increase from zero is less than required to reach the answer shown?

I don't really understand the question. As I said, the answer is the same whether the hole diameter is zero or any other figure (within the 'possible' limits). Can you perhaps clarify the question?

Kind Regards, John

 

[JohnW2]

(500/3)π cu cm, which is about 523.6 cu cm

Is there a reason you wrote it like that?

Yes, because I know that there are some pedantic people around here (see the post which follows yours ). If I had written 166.7π, someone may well have said that was 'inaccurate'. Similarly if I had written 166.67π, 166.66667π,or even 166.66666666666666666666666666667π - so I thought it 'safest' to put 500/3

Kind Regards, John

 

[TonyW2]

whether the hole diameter is zero or any other figure (within the 'possible' limits). Can you perhaps clarify the question?

Kind Regards, John[/quote]

If the 10cm "hole" measurement was progressively reduced to zero or the diameter of the "drill" first increased from zero. What would happen ?
How would the crossover from nothing to something--or vice versa--affect the situation?

 

[JohnW2]

Is this a sphere?

Is this a sphere:

Untitled

• JohnW2
• 17 Sep 2013
• 1

?

It's conceptually the sort of object one would get by drilling hole which ended up as 10cm long through a sphere of diameter 40cm.

If I told you that the outer diameter of that object was 40cm and that it's 'width' (up/down in the pic) ws 10cm, what would you say was the 'length of the hole' in the object?

Kind Regards, John

 

[JohnW2]

If the 10cm "hole" measurement was progressively reduced to zero or the diameter of the "drill" first increased from zero. What would happen ? How would the crossover from nothing to something--or vice versa--affect the situation?

I still don't really understand; there is no discontinuity between 'nothing' and 'something' - merely a progressive, continuous, change.

As for changing 'hole length', as you reduce it, the answer (amount of material left) will progressively reduce, eventually obviously becoming zero when the hole length was zero (which would also mean that the sphere diameter was zero) - however, you could get as close as you wanted to zero hole length and there would be a corresponding finite answer.

As for the drill diameter, as I said before, for a given 'hole length' the answer will be the same for any drill diameter (from zero to infinity) - the sphere diameter required to obtain the desired hole length will obviously increase as the diameter of the drill increases (from zero to infinity).

Is that any clearer?

Kind Regards, John

 

[EFLImpudence]

No, but it is not really spherical any longer, is it?

Wikipedia -
A sphere (from Greek σφαῖρα — sphaira, "globe, ball"[1]) is a perfectly round geometrical and circular object in three-dimensional space that resembles the shape of a completely round ball.

I don't know what the limit is before a sphere ceases to be a sphere.
A 1mm. diameter hole would obviously not have that effect.

I suppose I have to say the hole is 10mm. long but everything can be taken to the extreme to render an answer wrong and pointless.

A 10mm. drill in a 10cm. diameter sphere original question would leave nothing.
No sphere, no hole.

I still maintain that Bas' question was a puzzle or catch question with very little or no mathematics needed to arrive at an answer.
I had originally thought the answer to "what is the volume of the original sphere remaining?" may have been 'the same' or '100%' but because he said "what is the volume?" I thought an actual value was required.

 

[JohnW2]

No, but it is not really spherical any longer, is it?

Exactly - but, as I said, that's essentially what you'd get if you drilled a hole (which ended up) 10cm long though a 40cm sphere (and, don't forget, BAS's question said nothing about the diameter of the sphere).

I suppose I have to say the hole is 10mm. long but everything can be taken to the extreme to render an answer wrong and pointless.

But it's not 'extreme' - the whole point of the mathematical puzzle is that the answer remains the same for any combination of sphere size and hole diameter which resullt in a cylindrical hole of length 10cm.

A 10mm. drill in a 10cm. diameter sphere original question would leave nothing. No sphere, no hole.

That's very true, but nothing to do with the puzzle/problem - which requires that the hole be 10cm long. If you had a 10mm diameter drill, that would mean that the sphere would have to be a lot bigger than 10cm diameter for the hole length to end up as 10cm (can't be bothered to work out the exact sphere diameter ).

I still maintain that Bas' question was a puzzle or catch question with very little or no mathematics needed to arrive at an answer.

Well, only BAS can answer as to his intent, but if what you say were true (and I very much doubt it is), then he was talking about something totally different from the "hole through a sphere" mathematical problem/puzzle which has been around for best part of a century.

I had originally thought the answer to "what is the volume of the original sphere remaining?" may have been 'the same' or '100%' but because he said "what is the volume?" I thought an actual value was required.

Yes, but, using a 'sensible' (IMO) definition of 'the length of the hole' the answer you gave would only be correct if the drill/hole diameter was zero. I find it a little frustrating that you got the right answer on the basis of a major misinterpretation of the question (as I believe it was intended)!

Kind Regards, John

 

[EFLImpudence]

I find it a little frustrating that you got the right answer on the basis of a major misinterpretation of the question (as I believe it was intended)!

I have never claimed to have done other than work out the volume of a 10cm. sphere thinking it would not have changed.
I.e. drill entry to exit.

However, surely someone would have known if that was how the correct answer should/could have been calculated.

I have not come across this 'hole in sphere' before.

 

[JohnW2]

I have never claimed to have done other than work out the volume of a 10cm. sphere thinking it would not have changed.

Yes, I understand that, and I also understand 'where you are coming from'. As you have said, you are regarding it as a 'word puzzle' or 'trick question', and have taken the view (as you were doing with the plastic ball) that 'the volume of a sphere' remains unchanged even if material is removed by drilling holes through it. That's all fair enough but, as I said, that's not how this problem came into being - it's a genuine mathematical problem ('puzzle' if you like), not a 'party puzzle' based on ambiguities, words or 'tricks' ...

However, surely someone would have known if that was how the correct answer should/could have been calculated. I have not come across this 'hole in sphere' before.

Have you looked at the link which Detlef posted way back (page 2, I think) click here ??

Kind Regards, John

 

[EFLImpudence]

However, surely someone would have known if that was how the correct answer should/could have been calculated. I have not come across this 'hole in sphere' before.

Have you looked at the link which Detlef posted way back (page 2, I think) click here ??

I had seen it but not studied it, (I was busy yesterday) hence my mistake referring to it earlier.

That is what I meant above.
If it has been around for so long I am surprised that no one just knew the answer.
Presumably, had I not posted after my 'answer' that is what everyone would have thought about me.

 

[ban-all-sheds]

However, what if, in 1985 it had been asked on Newsnight "What was the Prime Minister's name in 1950?" ? - that would have been a definite ambiguity

Why?

 

[ban-all-sheds]

I still maintain that Bas' question was a puzzle or catch question with very little or no mathematics needed to arrive at an answer.

Well, only BAS can answer as to his intent, but if what you say were true (and I very much doubt it is), then he was talking about something totally different from the "hole through a sphere" mathematical problem/puzzle which has been around for best part of a century.

Your doubts are misplaced - EFLI is right.

The idea isn't that you solve it by complicated maths - the idea is that you deduce that the question would not be posed if the answer depended on the diameter of the sphere (and thus the diameter of the hole), therefore it must be constant for all sphere diameters ( ≥ 10cm), therefore the answer remains the same as the diameter of the sphere tends to 10 and the diameter of the hole tends to 0, therefore it's the volume of a sphere 10cm in diameter because at that point the hole has diameter 0 and no material is removed.

 

[JohnW2]

[That is what I meant above.
If it has been around for so long I am surprised that no one just knew the answer. Presumably, had I not posted after my 'answer' that is what everyone would have thought about me.

Exactly. I, for one, 'knew' the answer, as obvioulsy did BAS, and I presume that Detlef (and maybe others) also did, but there was no point in any of us just 'spewing it out' and spoiling it for everyone else. Also, as you imply, when you almost immediately produced a figure which 'happened' to be the correct answer (albeit arrived at by a totally 'wrong' process ), we probably all assumed that you also knew (I certainly presumed that) ... until, that is, you started writing too much!

Kind Regards, John

 

[JohnW2]

However, what if, in 1985 it had been asked on Newsnight "What was the Prime Minister's name in 1950?" ? - that would have been a definite ambiguity

Why?

You probably won't think so, because you don't seem to feel that the question is ambiguous. However, my comment was in response to what EFLI had said - that the ambiguity (which he accepted was there when it was a 'puzzle') would disappear if it were a 'serious question posed on Newsnight' because no-one would think that David Cameron had changed his name. I therefore pointed out that, had we been talking about a (the one and only!) female Prime Minister, then that argument as to why the ambiguity went away 'on Newnight' would no longer be valid.

Kind Regards, John

 

[ban-all-sheds]

If I had written 166.7π, someone may well have said that was 'inaccurate'. Similarly if I had written 166.67π, 166.66667π,or even 166.66666666666666666666666666667π - so I thought it 'safest' to put 500/3

Shame the forum doesn't support the necessary font.

So - lessons learned.

1) Rephrase the Q to specify that the sphere is a uniform solid with a density of 1g/cm³ and ask for the weight of the remaining object.

2) Pick a diameter which does not result in a repeating answer, e.g. 12cm.