Question

g A cylindrical tank with radius 7 m is being filled with water at a rate of 6 mଷ/min. How fast is the height of the water increasing? (Recall: V = πrଶh)

Answer 1

6/(49π) ≈ 0.03898 m/min

Explanation:

V = πr²h . . . . formula for the volume of a cylinder

dV/dt = πr²·dh/dt . . . . differentiate to find rate of change

Solving for dh/dt and filling in the numbers, we have ...

dh/dt = (dV/dt)/(πr²) = (6 m³/min)/(π(7 m)²) = 6/(49π) m/min

dh/dt ≈ 0.03898 m/min