Post a New Question

Calculus

posted by .

You have a conical tank, vertex down, which is 12 feet across the top and 18 feet deep. If water flows in at a rate of 9 cubic feet per minute, find the exact rate of change when the water is 6 feet deep.

You know the rate of dV/dt (inflow), and you can get the volume of a cone (1/3 h * toparea). So the trick is to write an equation relating top area to h (ie: toparea= PI*(12h/18)^2 /144 ) check that.

take the derivative of V with respect to h, and solve.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus-rate problem

    A conical tank (with vertex down) is 10 feet acros the top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep.
  2. calculus

    A conical tank( with vertex down) is 10 feet across the top and 18 feet deep. As the water flows into the tank, the change is the radius of the water at a rate of 2 feet per minute, find the rate of change of the volume of the water …
  3. Math

    A conical water tank with vertex down has a radius of 10 feet at the top and is 29 feet high. If water flows into the tank at a rate of 10 , how fast is the depth of the water increasing when the water is 17 feet deep?
  4. calculus

    A conical water tank with vertex down has a radius of 12 feet at the top and is 23 feet high. If water flows into the tank at a rate of 20 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 17 feet …
  5. cal

    A conical tank (with vertex down) is 12 feet across the top and 18 feet deep. If water is flowing into the tank at a rate of 18 cubic feet per minute, find the rate of change of the depth of the water when the water is 10 feet deep. …
  6. Calculus (math)

    A conical water tank with vertex down has a radius of 12 feet at the top and is 23 feet high. If water flows into the tank at a rate of 20 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 12 feet …
  7. math

    We did not find results for: a conical tank with its vertex down is 12 feet high and 12 feet in diameter at the top. water is being pumped in at the rate of 8 feet cubed per minute. find the rate at which the water level is rising …
  8. Math-How do I do this problem?

    An inverted conical tank (with vertex down) is 14 feet across the top and 24 feet deep. If water is flowing in at a rate of 12 ft3/min, find the rate of change of the depth of the water when the water is 10 feet deep.
  9. Math help, Please

    An inverted conical tank (with vertex down) is 14 feet across the top and 24 feet deep. If water is flowing in at a rate of 12 ft3/min, find the rate of change of the depth of the water when the water is 10 feet deep.
  10. math - calculus help!

    An inverted conical tank (with vertex down) is 14 feet across the top and 24 feet deep. If water is flowing in at a rate of 12 ft3/min, find the rate of change of the depth of the water when the water is 10 feet deep. 0.229 ft/min …

More Similar Questions

Post a New Question