The Pop Bottle
The bottom 3/4 of a pop bottle's total height is cylindrical in shape.
The upper 1/4 of the bottle's total height is irregular in shape and glass thickness.
The bottle is filled with rum up to (approximately) the halfway point of it's height.Keeping the lid on and using nothing but a ruler,how can you tell what percentage of the total volume of the bottle is filled with rum?
The upper 1/4 of the bottle's total height is irregular in shape and glass thickness.
The bottle is filled with rum up to (approximately) the halfway point of it's height.Keeping the lid on and using nothing but a ruler,how can you tell what percentage of the total volume of the bottle is filled with rum?
posted by Knightmare at
5:23 PM
10 Comments:
For cyllinder
Vfull=Pi*r^2*h1
This is the filled space in the bottle.
H1 is from bottom of bottle to top of liquid.
Flip bottle upside down:
H2 is from top of bottle (formerly the bottom), to the top of the liquid.
This is the empty space in the bottle.
Vempty=Pi*r^2*h2
%full=Vfull/Vbottle=Vfull/(Vempty+Vfull)
%full= Pi*r^2*h1/( Pi*r^2*h1+ Pi*r^2*h2)
%full=h1/(h1+h2)
We can use rule to measure H1 and H2
Cam
Cam...your too good
i thought for sure that this would last for awhile.
When the rum is at the bottom, measure the height h1 of the rum in the cylinder. Turn over, and measure the height h2 of the air in the cylinder. The heights are proportional to the volumes of the air and rum. So the fraction that is rum to the total is h1/(h1+h2). Times 100 for %.
Well I know I wouldn't get it
(same as the simplify and steel ball in mercury)
Beaten to it again :( Nice problem, reminiscent of the round trip one, but quite a different bit of logic. It feels like a pucker classic logic problem.
My first thought:
No rum, it's Pop!
I would prefer to drink shots of the rum until there was none left. Then if you remember how many you had, multiply that by the volume of the shot.
Maybe it's a language difference. To me, pop is a soft drink like Coke, Pepsi, or soda water etc.
Rum is an alcoholic drink, usually only consumed by old people.
My 4 hr gambling addiction has bought me to this game a little late.
I would like to point out that Cam, who came storming in with a good answer has missed out one vital step in his method. This would lead to incorrect values...
He didn't put the lid on the bottle, turning it upside down would be a waste of rum....;-)
Pop? Que? My wife, the font of all knowledge say it is from "Popular Beverage"....?
Ah bugger, just re-read the question..... lid on bottle.
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