A 24ft high conical water tank has its vertex on the ground and radius of the base is 10 ft. If water flows into the tank at a rate of 20 ft3/min, how fast is the depth of water increasing when the depth of the water is 20 ft?
calculus - MathMate, Tuesday, October 19, 2010 at 12:09pm
The vertex is on the ground, so the tank is in a funnel position.
Let the water height be h, then the radius of the surface of water is r(h)=10h/24=5h/12
The volume at a height of h is
Differentiate with respect to time, t
Since dV(h)/dt is known (=20 ft³/min), you can solve for dh/dt.
Note that the unit of dh/dt is in ft/min.