Question 1052104: An empty swimming pool is in the shape of a rectangle 10 meters long, 5 meters wide and 1 meters deep. A child starts to fill the pool using a saucepan with a circular base having a diameter of 20cm and a depth of 10cm. The child can fill the saucepan and empty it into the pool twice per minute. How many days would it take the child (working 24 hours per day) to fill the pool? Don't round to the nearest day.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the volume of a rectangular pool is l * w * h.
l = length = 10 meters
w = width = 5 meters
h = height = 1 meters
the volume of the pool is 10 * 5 * 1 = 50 cubic meters.
the volume of a cylindrical saucepan with a circular base is equal to pi * r^2 * h.
the radius is equal to half the length of the diamter, therefore:
r = radius = 1/2 * 20 = 10 cm.
h = height = depth = 10 cm.
you want to convert everything to meters, or convert everuything to centimeters.
we'll convert everything to centimeters.
the rectangular pool is 10 * 5 * 1 meters.
since there are 100 centimeters in a mater, the rectangular pool is 1000 * 500 * 100 centimeters.
the volume of the pool is therefore 1000 * 500 * 100 = 50 million cubic centimeters.
the volume of the saucepan is pi * r^2 * h which is equal to pi * 10^2 * 10 = 3141.592654 cubic centimeters.
divide 50 million by 3141.592654 and you get 15915.49431 full saucepans required to fill the pool.
divide that by 2 saucepans per minute and you get 7957.747155 minutes.
divide that by 1440 and you get 5.526213302 days.
to confirm, start with the volume of one saucepan.
the volume, in centimeters is equal to pi * 10^2 * 10 = 3141.592654 cubic centimeters.
the child can put two of these in the pool every minute.
therefore the child can put 3141.592654 * 2 = 6283.185307 cubic centimeters in the pool every minute.
in 7957.747155 minutes, the child can therefore put 7957.747155 * 6283.185307 = 50 million cubic centimeters in the pool.
7957.747155 / 1440 = 5.526213302.
the solution is confirmed.
the solution is that it will take the child 5.526213302 days to fill the pool if the child is working 24 hours a day.
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