The Great Volume 1
Geometry
Level
2
Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Find the time (in hours) in which the level of water in the tank will rise by 21 cm.
The answer is 2.
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1 solution
The volume of water flowing through the pipe at any time t is expressible as:
V(t) = (pi*r^2) * (15000 m/hr) * t = [pi * (0.07 m)^2] * (15000 m/hr) *t (i).
We wish to know at what time t (in hrs) the tank reaches a height of 21 cm, or when the filled volume reaches 50 m * 44 m * 0.21 m = 462 m^3. Equating (i) with 462 m^3 and solving for t gives:
t = 462 m^3 / [pi * (0.07 m)^2 * 15000 m/hr] = 2 hrs.