Bottle Trouble
So Mr. Ketuchky decided to double all the dimensions of a One Litre bottle, can you tell me what is the volume of the new bottle ?
Labels: thinktank
posted by Rajesh Lal at
11:27 PM
Tuesday, June 2, 2009
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12 Comments:
Hello,
When you say 'double all the dimensions' can you confirm you mean the just the 3 main ones for volume; height, width and depth; or do we need to include time and space (plus any others there might be)?
Cheers
assuming you are speaking of the three spacial dimensions, the answer would be double the volume 3 times or (original volume)^3 which equals 16L's
the bottle's volume would be quadrupled from the original
The new volume of the bottle is now 8 Liters. You must double the volume 3 times.
yes,
Including the time dimension, it would be 8 liters.
2*2*2 = 8
its not 8litres,cos its a bottle not a cube or cuboid.
this question is near enough imposible to answer, you would have to mesure all parts of the bottle, vork out the volume, which would be very hard because of the 5 bumps at the base of the bottle and the curved top, i hav no idea of what the answer is but if i had to guess i would go for:
if you double the length, width, height that would be
(height*2)+(length*2)+(width*2)
so the orignal (1 litre) if you doble any of the 3 things above(h, l, w)
original bottle's width*2 = 2 litre bottle
2 litre bottle's length*2 = 4 litre bottle
4 litre bottle's hight*2 = 8 litre bottle
8 Litre bottle
It is 8 liters. Let's call the original radius r and the original height h. The volume of the bottle would be pi*r^2*h=1. If r and h were doubled, then the volume would be pi*(2r)^2*(2h), or 8*pi*r^2*h=8.
i got 80L...
pretty sure that is right. i'f im right i'll explain my method. in a hurry now...
8L - easy peasy
step by step solution
volume, 1=pi*r^2*L
double dimens. =pi*(2r)^2*2L
=pi*(2^2*r^2)*2L
=pi*(4*r^2)*2L
=4*2(pi*r^2*L)
=8*(pi*r^2*L)
b/c pi*r^2*L= 1L
8*1L = 8L
It completely depends on the type of bottle. If it's a cylindrical bottle, or a cube bottle, or who knows what shape- Mr. Kentucky seems to imply alcohol, which comes in all sorts of fancy bottle shapes
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