Or "What was the Prime Minister's name in 1971?"
Monty Hall
- Thread starter ebee
- Start date
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LOL.
Good un
Good un
"The other schoolboy howler was "what date is Christmas day in Australia"
25th June came up quite often"
LOL.
Like when people ask my age age I tell `em "X years old but on Christmas Day I will be X + 1 ", the ask if my birthday is on on Christmas day & I reply "No, 25th June!"
25th June came up quite often"
LOL.
Like when people ask my age age I tell `em "X years old but on Christmas Day I will be X + 1 ", the ask if my birthday is on on Christmas day & I reply "No, 25th June!"
I'm afraid you still haven't got it. There is a finite answer to the puzzle which is exactly the same for any 10cm long hole of any diameter, provided only that the diameter of the original sphere was not less than 10cm.
No. No-one said anything about the drill only being 10cm long. It is the length of the hole after drilling that is 10cm. If the sphere started off as 20cm, 40cm, 100cm, 1000cm or whatever in diameter, if one had a drill of adequate diameter and length, one could drill a hole through the sphere which (after drilling, hence removal of all the 'excess material' in the 'domed cap') ended up with a length of 10cm.
What is not specified in the puzzle? The answer can be specified, and there is only one, not an infinite number. Provided only that the sphere did not have a diameter less than 10cm, the answer will always be 166.67π cu cm, regardless of the diameter of the hole.
No. As above, there is only one answer - whether the hole is of zero or finite diameter. As I said, provided only that the sphere did not have a diameter less than 10cm, the answer will always be 166.67π cu cm, regardless of the diameter of the hole (and the sphere).
Does that help at all?
Kind Regards, John
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Indeed, that's what a said a few posts back - I very much doubt that it's a mathematical co-incidence, and therefore suspect that there is a conceptual explanation.
As I said, another way of looking at it is that the volume of material removed is always exactly the right amount to make a hollow sphere, whose outer diameter is the same as the original sphere, and whose wall thickness is equal to the diameter of the sphere minus the length of the hole. I can't help but feel that the 'conceptual answer' is probably related to that!
Kind Regards, John
Kind Regards, John
(grumpy old man speaking!) was he actually born then?
However, this is another example of 'lack of clarity' in the question. It's actually totally ambiguous - so 'either' answer is, I suppose, correct.
Kind Regards, John
I haven't studied all of the above.
However, what about this?
Why does the 10cm. long hole have to have right angled ends?
The sphere is 10cm. in diameter.
So, from drill touching the sphere to drill exiting the sphere is 10cm.
The shape of the drill end may involve 'finishing off' the hole but this would be the same in a cube so you can't count that.
Therefore the hole must be 10cm. long but it has domed ends.
After all, a hole is just where any solid material has been removed.
Measuring the length of the hole by discounting the (in this case, domed) ends would not be correct.
However, what about this?
Why does the 10cm. long hole have to have right angled ends?
The sphere is 10cm. in diameter.
So, from drill touching the sphere to drill exiting the sphere is 10cm.
The shape of the drill end may involve 'finishing off' the hole but this would be the same in a cube so you can't count that.
Therefore the hole must be 10cm. long but it has domed ends.
After all, a hole is just where any solid material has been removed.
Measuring the length of the hole by discounting the (in this case, domed) ends would not be correct.
Got it? Yes thanks.
I hadn't realised the relationship with the cord length and the drill diameter couldn't change doh!
I do maintain however that the logic of a 10cm zero diameter hole through an axis does mean that the sphere is 10cm diameter - I never mentioned a drill at all. You can't have a hole outside the sphere and anything less than 10cm would not go through so how could the sphere be anything other than 10cm ? This doesn't alter the correctness of your answer, but I don't think that the logic in this specific instance was wrong.
I hadn't realised the relationship with the cord length and the drill diameter couldn't change doh!
I do maintain however that the logic of a 10cm zero diameter hole through an axis does mean that the sphere is 10cm diameter - I never mentioned a drill at all. You can't have a hole outside the sphere and anything less than 10cm would not go through so how could the sphere be anything other than 10cm ? This doesn't alter the correctness of your answer, but I don't think that the logic in this specific instance was wrong.
Because that's what you will end up with after you have drilled a hole all the way through the sphere
Eh? No-one told you that. As I keep saying, the whole point is that the answer will be the same for any sphere diameter ≥10cm.
Only if the sphere were 10cm in diameter (and hence the hole of zero diameter). From drill touching sphere to drill exiting sphere will,of course, always be equal to the diameter of the sphere - which, as I've said, could be anything above 10cm.
NO. You're trying to make it even more confusing than it is! We are not talking about 'where any solid material has been removed'. We're talking about the cylindrical hole (with 'square ends') which exists in the object after the drilling has taken place. If the sphere is a lot bigger than 10cm diamter, then the amount of material removed could be a hell of a lot more than the volume of the hole you ended up with.
Why on earth not? As I say, you seem to be adding confusions. If I just handed you the finished object, with the hole drilled through it, and asked you how long the hole was, you would surely simply measure the hole you could see, wouldn't you? Indeed, you wouldn't even know for sure what shape the object had been before the hole was drilled, so you wouldn't be able to determine 'how much material had been removed' even if you wanted to!
Kind Regards, John
Great!
Ah. Yes, for any given diameter of sphere, there's obviously only one hole diameter which will result in a 10cm long hole - is that what you mean?
No-one is denying that - as you say, if the hole is of zero diameter, then the sphere would have to be 10cm - but zero diameter is just one case out of an infinite number of possibilities. As above, if you tell me any other hole diameter, I'll tell you what the sphere diameter has to be for the hole to be 10cm long. A zero hole diameter is just one possibility out of the infinite number of possibilities.
You're again thinking of the length of the drill, not of the hole you end up with. If you drilled a hole (of the one appropriate diameter) which ended up 10cm long through a sphere of 20cm diameter, you'd obviously need a drill which was at least 20cm long, but once you'd drilled that hole, hey presto, you'd find that it was 10cm long (provided you'd got the diameter right!!).
Kind Regards, John
How deep is a hole in the ground which has a curved bottom?
That obvioulsy depends upon how one has defined depth.
The same issue does not arise with the puzzle. The object one ends up with (c.f. your hole in the ground) simply has a hole (without curved/domed ends), so there is only one option as to what one regards as 'the length of the hole' (in the drilled object).
If you're going to try to invoke the material which was removed in order to create the hole, then, with your hole in ground, what if, prior to digging, there had been a 6 feet high mound of soil above the position of the finished hole. Would you then say that the hole was 6 feet deeper than it actually was (relative to 'ground level')?!!
Kind Regards, John
The digger may think so but you have added a get-out proviso - relative to ground level
Were the mound large enough the we are back to square one..
Were the mound large enough the we are back to square one..
Yes, but I added that proviso for a reason. The point is that, with both the sphere (after drilling) and the hole in the ground (after digging), all evidence of the material removed in order to arrive at the situation you are presented with (an oblate spheroid with a hole though it, or a hole in the ground) will have disappeared - i.e. you won't know that the object started life as a sphere, or that there had been a mound of earth above the place the hole was dug.
As I said, I think you're making it unnecessarily complicated. The puzzle just relates to the object 'as it is' after the hole has been drilled.
Kind Regards, John
Yep agreed.
It`s sometimes difficult either to explain or understand in words only.
Pictures often make it easier.
But the best way would to be for someone to make the shapes out say wood and compare them as this = that= tother.
ie a 10cm soild sphere, a 20 cm sphere with the hole thru it an 10 cm
and a 15 cm sphere.
Were they all in front of you to inspect, weigh and measure volume by displacement in a bucket of water then the idea would click into place.
Unfortunately, we do not have that luxury here.
It`s sometimes difficult either to explain or understand in words only.
Pictures often make it easier.
But the best way would to be for someone to make the shapes out say wood and compare them as this = that= tother.
ie a 10cm soild sphere, a 20 cm sphere with the hole thru it an 10 cm
and a 15 cm sphere.
Were they all in front of you to inspect, weigh and measure volume by displacement in a bucket of water then the idea would click into place.
Unfortunately, we do not have that luxury here.
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