Answer:
5 cm
Explanation:
You want to know the radius of a drain pipe that empties a cylindrical tank of height 20 cm and radius 30 cm in 2 minutes when the flow rate is 6 cm/s.
Flow rate
The rate of emptying the cylindrical tank is its volume divided by the time it takes to empty.
V = πr²h
V = π(30 cm)²(20 cm) = 18000π cm³
If this volume is drained in 2 minutes = 120 seconds, the flow rate is ...
(18000π cm³)/(120 s) = 150π cm³/s
Drain area
The area of the drain pipe can be found by dividing this volumetric flow rate by the speed of the flow:
(150π cm³/s)/(6 cm/s) = 25π cm²
Drain radius
The radius of the drain pipe is that of a circle with area 25π cm²:
A = πr²
25π cm² = πr²
r² = 25 cm² . . . . . divide by π
r = 5 cm
The radius of the drain pipe is 5 cm.
__
Additional comment
The 20 cm height of the tank is emptied in 120 seconds, so the rate of change of height is 20/120 = 1/6 cm/s. The exit pipe has a flow rate of 6 cm/s, which is 6/(1/6) = 36 times the rate of change in the tank.
The height change is inversely proportional to the area, which is proportional to the square of the radius. So the radius ratio is √36 = 6, meaning the drain must have a radius of (30 cm)/6 = 5 cm.