How Fast is the Water Level Dropping in the Tank?

[Mitchtwitchita]

Water is leaking out of a cylindrical tank , with circular base radius 0.8 m at the rate of 0.2 m3/min. The water level is falling at ...? ..m/min. What is the question mark? (Hint: the radius does not change)

V=(pi)r^2h, dV/dt = 0.2, r = 0.8 ?

Can anyone give me a hand in getting this one started?

 

[HallsofIvy]

Differentiate both sides of V= (pi)r^2 h, remembering that "the radius does not change". Since h is the "water level", "the rate at which the water level is falling" is dh/dt.

 

[Mitchtwitchita]

So, dV/dt = (pi)r^2*dh/dt
0.2 = (pi)(o.8)^2*dh/dt
dh/dt =0.0995 ?

Hypothetically, how would you solve for volume if the rates of change of the height and radii are given, as well as the radius and height when the derivative would seem to cancel the h in the equation?