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Guest Message by DevFuse

# Hole in a sphere

Best Answer bonanova, 23 August 2007 - 07:11 AM

The volume of the spherical caps is given by:
[list]
where
[list]
[*] h = the height of the cap (difference between r and the distance from the centre of the[/*:m:1cc31][list] sphere to the centre of the circular end of the hole)

Kudos to cpotting for the cap formula.
Spoiler for Here's the mathematical solution
Spoiler for Here's the logical solution
Go to the full post

166 replies to this topic

### #121 andromeda

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Posted 17 July 2010 - 05:47 PM

I haven't read the whole thread, so I don't know if is this has been posted before...

Spoiler for ...

edit: grammar

Edited by andromeda, 17 July 2010 - 05:48 PM.

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### #122 bonanova

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Posted 18 July 2010 - 03:43 AM

Spoiler for I like this puzzle!

Dej Mar

Thanks for adding this great poetic version of the puzzle!

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Vidi vici veni.

### #123 sak_lko

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Posted 21 July 2010 - 07:10 AM

Spoiler for logical way is easy

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### #124 NickFleming

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Posted 21 July 2010 - 12:42 PM

Maybe this has already been posted. A friend asked me this a while back, and I answered her in less than a minute.
She said I was a genius. But I said there were two ways to arrive at the answer, and I simply chose the easier way.

A 6-inch
[long] hole is drilled through a sphere.
What is the volume of the remaining portion of the sphere?

The hard way involves calculus. The easy way uses logic.

What is the circumference of the six inch hole? Wide drill bit, thin drill bit, what?
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### #125 NickFleming

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Posted 21 July 2010 - 12:44 PM

I haven't read the whole thread, so I don't know if is this has been posted before...

Spoiler for ...

edit: grammar

EUREKA! If you know your scientific history, you'll know what I mean. Only problem I see with this is that what is asked for is the answer, not the process to the answer.
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### #126 sak_lko

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Posted 21 July 2010 - 01:58 PM

What is the circumference of the six inch hole? Wide drill bit, thin drill bit, what?

Spoiler for redius of the hole

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### #127 NickFleming

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Posted 21 July 2010 - 03:12 PM

Spoiler for redius of the hole

You can't really assume anything. And a hole is defined as an "unoccupied space." Hardly fits.
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### #128 Arbelle

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Posted 21 July 2010 - 04:09 PM

What is the circumference of the six inch hole? Wide drill bit, thin drill bit, what?

The circumference (and thanks for teacing me that word) depends on the size of the sphere. It will be different for different sizes of spheres. And despite your reservations, it was a good advise you got, to assume a zero circumference. Even if it, technically, won't be a real hole.
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### #129 NickFleming

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Posted 21 July 2010 - 04:20 PM

No, because for instance the drill bit used to drill the hole could vary dramatically, thus affecting the volume taken away from the sphere.
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### #130 Arbelle

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Posted 21 July 2010 - 05:17 PM

Spoiler for I know, but

No, because for instance the drill bit used to drill the hole could vary dramatically, thus affecting the volume taken away from the sphere.

I once read a similar two-dimentional riddle, I'll try to find it and post it.
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