SOLUTION: a roof with an area of 200m square collects rain into a 4 metre diameter tank. If 100mm of rain falls how much water is collected in metres cubed and how many cm will the water ris

Algebra ->  Volume -> SOLUTION: a roof with an area of 200m square collects rain into a 4 metre diameter tank. If 100mm of rain falls how much water is collected in metres cubed and how many cm will the water ris      Log On


   

Question 898369: a roof with an area of 200m square collects rain into a 4 metre diameter tank. If 100mm of rain falls how much water is collected in metres cubed and how many cm will the water rise in the tank
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
1mm rain means that every square meter covered with water with the height of 1mm.
One meter is 1000mm, so the total volume is 1000 x 1000 x 1 = 10^6 cubic mm or 10^3 cubic cm or 1 cubic dm, which is one liter.
So for every mm of rain you get one liter per square meter.
200 m^2 by 1 mm you get 200 liters
100 mm means you get 200 * 100 liters =20000 liters= 20 m^3
diameter of tank = 4 m
radius = 2m
height of water = h
Volume = pi * r^2 * h
20 = pi * 2^2*h
20/4pi = h
15.07 m
1507 cm