SOLUTION: The rain that falls on a house roof 11m x 6.75m is channeled into a cistern that is 2.5m in diameter. How much rainfall on the roof would it take to fill the cistern to a depth of

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Question 553649: The rain that falls on a house roof 11m x 6.75m is channeled into a cistern that is 2.5m in diameter. How much rainfall on the roof would it take to fill the cistern to a depth of 2m? I can calculate the amount water in the cistern but can't figure out the amount of rainfall needed on the roof. Thank you
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You need to find the volume of water in the cylindical cistern which have done already.
This should come to:
V+=+pi%2Ar%5E2%2Ah or
V+=+pi%2A%28D%2F2%29%5E2%2Ah Substitute: D = 2.5, h = 2.
V+=+pi%2A%282.5%2F2%29%5E2%2A2
V+=+pi%2A%286.25%2F4%29%2A2 Use pi+=+3.14 as an approximation.
V+=+9.8125
To find the volume of rain falling on the roof (presumably a flat roof), mulltiply the area by the depth of the accummulated rain water (d).
V+=+11%2A6.75%2Ad
V+=+74.25%2Ad Substitute V = 9.8125 from step 1.
9.8125+=+74.25%2Ad Divide both sides by 745.25
d+=+7.56688 inches of rain.