calculus

posted by .

grain is being poured through a chute at rate of 8 ft^3/min and forms a conical pile whose radius of the bottom is always 1/2 the height of pile. How fast is circumference increasing when the pile is 10 feet high?

  • calculus -

    given:
    r = (1/2)h
    2r = h

    Let V be the volume

    V = (1/3)π r^2 h
    V = (1/3)π(r^2)(2r) = (2/3)π r^3
    dV/dt = 2πr^2 dr/dt
    when h = 10, r = 5
    8 = 2π(25)dr/dt
    dr/dt = 4/(25π)

    Let circumference be C

    C = 2πr
    dC/dt = 2π dr/dt
    so at that instance,
    dC/dt = 2π(4/(25π) = 8/25 ft/min

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. AP Calculus

    Wheat is poured through a chute at the rate of and falls in a conical pile whose bottom radius is always half the altitude. How fast will the circumference of the base be increasing when the pile is 8 ft high?
  2. 12th grade

    Wheat is falling from a chute onto a level floor at a rate of 8pi ft3/min to form a conical pile. If the height of the pile is always equal to the radius of its base, at what rate is the radius increasing when the pile is 8 ft deep?
  3. Math

    Corn is poured through a chute at the rate of 10ft^3 / min and falls in a conical pile whose bottom radius is always half the height. How fast is the circumference of the base changing when the pile is 8 feet high?
  4. Calculus: free body diagram--PLZ HELP!=)

    Grain is being poured through a chute at a rate of 8 cubic feet per minute and forms a conical pile. The radius of the bottom of the pile is always half of the heightof the pile. How fast is the circumference of the base increasing …
  5. Timerate problem(calculus)

    Sand is being dropped at the rate 10 metercube/min onto a conical pile. If the height of the pile is always twice the base radius, at what rate is the increasing when the pile is 8 m high?
  6. Calculus

    Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing …
  7. Calculus

    Wheat is poured through a chute at the rate of 10 ft^3/min and falls in a cone-shaped pile whose bottom radius is always half its height. How fast is the height of the cone increasing when the pile is 8 feet high?
  8. Calculus 1

    Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing …
  9. calc

    Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile …
  10. Calc

    Gravel is being dumped from a conveyor belt at a rate of 20 {\rm ft}^3{\rm /min}. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing …

More Similar Questions