SOLUTION: Rainwater from a flat roof 44m x 12m flows into a cylindrical tank of diameter 4m. What is the increase in the depth of water in the tank if 5mm of rain falls? Thanks!

Question 474410: Rainwater from a flat roof 44m x 12m flows into a cylindrical tank of diameter 4m. What is the increase in the depth of water in the tank if 5mm of rain falls?
Thanks!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
volume of the water on the roof is equal to h1 * a1 where h1 is the height of the volume of water on the roof and a1 is the area of the base of the roof.
volume of the water in the tank is equal to h2 * a2 where h2 is the height of the volume of water in the tank and a2 is the area of the base of the tank.
the area of the base of the roof is equal to 12 * 44 = 528 square meters.
the area of the base of the tank is equal to pi*r^2 which is equal to pi*2^2 which is equal to 4*pi.
the volume of water on the roof is therefore equal to .005 * 528 = 2.64 cubic meters.
the volume of water in the tank is therefore equal to h2 * 4 * pi.
since the volume in the tank and the volume on the roof is the same, then these equations can be made equal to each other so you get:
2.64 cubic inches = h2 * 4 * pi.
divide both sides of this equation by 4 * pi and you get:
2.64 / (4 * pi) = h2
solve for h2 and you get:
h2 = .210084525 meters.
h1 was given in millimeters which we converted to meters by dividing by 1000 to get .005 meters.
h2 is given in mters which we can convert to millimeters by multiplying by 1000 to get 210.084525 millimeters.
the general formula used to solve this problem would be:
h1 * 528 = h2 * 4 * pi
if we know h1 (height of the water on the roof), then we can solve for h2.
if we know h2 (height of the water in the tank), then we can solve for h1.

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