Expert: Ahmed Salami - 7/14/2010

Question
Water flows into a vertical cylindrical tank a 12 cu. ft. per min.; the surface rises 6 in. per min. Find the radius of the tank.

Answer
Hi Avenrose,
The volume of water V in a vertical cylindrical tank depends on the water level h and the radius r according to the formula;
V = πr²h
As water flows into the tank, the volume and water level change but not the radius and so r is constant. Finding derivatives,
dV/dt = (πr²)dh/dt
But,
dV/dt = 12 cu.ft/min and dh/dt = 6 in/min = 0.5 ft/min
So,
12 = (πr²)0.5
πr² = 24
r² = 24/π
r = √(24/π)
 = 2.8 ft

Regards