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In the middel of a round pool lies a beatiful water-lily .Th

Sat Nov 21, 2009 6:59 am  by tartle

In the middel of a round pool lies a beatiful water-lily .The warer-lily doubles in size every day .
After exactly 20 days the complete pool will be covered by the lily. After how many days will half of the pool be covered by the water-lily????
Sun Nov 29, 2009 4:54 pm  by GrassMan

Lets go backwards instead of counting from day 1..2 and so on.
On day 20th, the lily is so big that it covers the entire pool. The lily doubles every day (GIVEN). That means the lily must cover half of the pool, a day before it covers the entire pool (i.e. Day 20th). So it will cover half of the pool on the 19th Day. What Say PPl?

Tha Answer: - Day no 19. :P
Wed Sep 01, 2010 10:50 pm  by Physics0

When you say doubling, do you mean the lily is doubling in radius every day, but half of the surface area needs to be covered?

If that's true, then the solution is a little harder.

A=pi * r^2 is the formula for the area of a circle. To find the number of days that it would take to reach half the total area, we need to know in what manner the area of a circle changes when the radius changes. It is pretty simple to deduce that if we multiply r by a number, then A will change by a factor of that number squared. We will call the radius of our pool r. Because we want the area of the pool to be reduced by a factor of 2, we need to reduce r by a factor of root 2, giving us r/√2 for the radius of our lily.
How many days will it take for the lily to reach this place? More than 19, less than 20. At this point we must speculate about how the lily grows in a matter of hours.
As far as I can tell, if increase in radius of the lily is a smooth curve, the answer should be 19 days, 12 hours.

Wonderful problem, it really made me think.
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