An Everyday Scenario
You have a bottle containing some water. Assume the bottle is transparent so that you can observe the water level. You are also given a rubber-band. Can you determine if the bottle is more than half (in volume) full or less than half full ? There are no restrictions on the shape of the bottle. You aren't allowed to use anything else to measure the water level.
I will take a cubic bottle (easiest you say. Well I am the first person to give a solution I surely should have it easy). I will use the rubber band to measure one edge. Fold the rubber band in half to find the center of that edge and then put the rubber band around the cube to mark the half the volume. Now I will pour water into this marked transparent cubic bottle as I watch (From a normal to avoid parallax error) the water level rise to match the rubber band's level. So there you have half the volume of the cube filled. The same can be done with a sphere but it is easier to find the center of a cube with a rubber band. Cylinders are good too with the filling being done from one of the circular surfaces.
ReplyDeleteRafiki - That is an interesting method!:-) However it does not generalize to bottles with varying cross-sections!
ReplyDeleteWhoa! What a pace!! Looks like I've to stay up in the night to have a go at something :))
ReplyDeleteJust kidding :)
I think we are depending on some kind of symmetrical cross-section.. horizontal/vertical/diagonal and then we can tie the rubber band across that line of symmetry and tilt the bottle along that line (try to avoid parallal error as Rafiki mentioned :-D) to know whether it is more than half full or not... Not really sure! If this is an everyday scenario, I wonder how we survive every day with such ignorance :-O :-D
ReplyDeletePut the rubber-band around the bottle to mark the the lavel of water.Then invert the bottle(assuming it has a lid to close). If the water level is not upto the rubber-band's level, that is some empty space between the water-level and the rubber-band level, you can infer that volume of water is less than half the volume of the bottle.
ReplyDeleteWhen inverted, if the water -level goes above the rubber-band level , then water is more than half the volume of the bottle. If the levels coincide , it ia exactly half
Anonymous - We assume vertical symmetry, but actually even that we only kind of assume in a rough way :-)
ReplyDeleteKamala - Thanks for visiting his blog, and for the comment! That was a brilliant answer ! Exactly what I was looking for :-)
ReplyDeleteThe rubberband is not really needed. You could just as well use your fingers. I put it in to distract the reader, and to bring in some style quotient into the problem !:-)
So the point is rubber bands are stylish. :P
ReplyDelete