Guest Posted August 13, 2011 Report Share Posted August 13, 2011 There was once an empty room.. with nothing inside but walls.. and a huge hole on the top of the ceiling Then water started coming out of the hole.. filling the room.. during the first 5 minutes.. the height of the water is only 1cm.. and in the next 5 minutes.. the height of the water is doubled.. 2 cm.. another 5 minutes.. the height is again doubled.. which is 4 cm.. the next 5 minutes.. guess what? the height is 8 cm... and..so on... after a full 100 minutes.. the room is totally filled with water.. How long does it take for ONLY HALF of the room to be filled with water? Answer in how many minutes.. and why.. Note : we don't know the height of the room...... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 13, 2011 Report Share Posted August 13, 2011 it would take 95 minutes for the room to be half empty :-) we know that the level gets doubled in every 5 minutes so if it's 50% it would take 5 minutes to get doubled and so it would become 100% and if need height it would be 2^19. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 13, 2011 Report Share Posted August 13, 2011 99 min Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 13, 2011 Report Share Posted August 13, 2011 no i wrote it wrong, it is 95 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 13, 2011 Report Share Posted August 13, 2011 The water is doubling every five minutes. Since the room is filled in 100 minutes, it will be half full in 95 minutes. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 13, 2011 Report Share Posted August 13, 2011 95 minutes. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 13, 2011 Report Share Posted August 13, 2011 It would take 95 minutes as everyone has noted. And the room is 5.24288 kilometers high, and is most likely a cone shape with the pointy end on top and has a slope that is the square root of 2 I think. If I am right, that means the base of the cone has radius of 7.414 km and volume would be 301 cubic km of water? So it was filling at a rate of 3 cubic km per minute? Is that right? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 13, 2011 Report Share Posted August 13, 2011 ya its 95.. Quote Link to comment Share on other sites More sharing options...
0 Smith Posted August 13, 2011 Report Share Posted August 13, 2011 (edited) Nana, your proposal regarding the shape of the room makes sense assuming that the rate of flow of the water is constant, but that was not stated. I would probably want to make that assumption as well, honestly. I like your deduction about the conical shape given a regular flow rate and the exponential increase in height - though I did not check the math on the slope of the wall. However, the OP included a "huge hole in the top of the ceiling". I think that your conical room could not include the huge hole AND be filled as stated without some adjustment to either the base diameter of the cone, the slope of the walls, the geometry of the shape (changing slope - not a true cone), or the rate of water flow. Nonetheless, yours was the most complete answer so far to an "easy-peasy" question (I'm surprised there was no use of the phrase "easy-peasy" yet). Note to the newbies - strive to use "Spoilers" so that others can THINK before they see YOUR answer. That's the purpose here, to think, AND have fun. Edited August 13, 2011 by Smith Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 13, 2011 Report Share Posted August 13, 2011 Smith, yes, the base would need to expand in relation to the size of the hole at the top. And since the largest manmade structure is only a bit more than 800 meters high, the size of this room is comparable to the largest mountains on Earth rather than to anything anybody ever made. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 14, 2011 Report Share Posted August 14, 2011 This really a tall room, 1048575 cm, 34402 feet or 6.51553 miles, I would believe that any water at the top of this room would be frozen and not drain into the room. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 14, 2011 Report Share Posted August 14, 2011 Yup.. I think everyone's correct.. and yes.. it's a very very VERY tall room.. sorry for posting such an easy question....... thanks for answering though .. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 14, 2011 Report Share Posted August 14, 2011 It's probably not conical. Assuming constant flow, the incremental height of the water's surface increases inversely as the area of its surface. Since the water's surface is rising exponentially [constant ratio at fixed intervals of time and thus fixed added volume of water] the shape of the room is such that its cross sectional area is decreasing exponentially with height. For a single sloping wall there would be a linear decrease - not enough. For a conical shape, there would be a quadratic decrease - but that's still not enough. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 14, 2011 Report Share Posted August 14, 2011 99 min srujana Quote Link to comment Share on other sites More sharing options...
Question
Guest
There was once an empty room.. with nothing inside but walls.. and a huge hole on the top of the ceiling
Then water started coming out of the hole.. filling the room..
during the first 5 minutes.. the height of the water is only 1cm..
and in the next 5 minutes.. the height of the water is doubled.. 2 cm..
another 5 minutes.. the height is again doubled.. which is 4 cm..
the next 5 minutes.. guess what? the height is 8 cm...
and..so on...
after a full 100 minutes.. the room is totally filled with water..
How long does it take for ONLY HALF of the room to be filled with water?
Answer in how many minutes.. and why..
Note : we don't know the height of the room......
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