Calculus

posted by .

Sand is poured onto a level piece of ground at the rate of 0.25 m^3/min and forms a conical pile whose height is equal to its base diameter. How fast is the height increasing at the instant when the height is 0.50 m? V = 1/3(pi)(r^2)h

I got 3/pie, is that correct?

  • Calculus -

    I got 4/π

    let the radius be r, then the height is 2r
    V= (1/3)πr^2 h
    = (1/3)πr^2(2r)
    = (2/3)πr^3
    dV/dt = 2π r^2 dr/dt
    when 2r=.5
    r = .25 and dV/dt = .25

    1/4 = 2π(1/16) dr/dt
    times 8
    2 = π dr/dt
    dr/dt = 2/π
    d(2r)/dt = d(height)/dt = 4/π

  • Calculus -

    Thank you!

  • Calculus -

    Where did you get 8 from?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. AP Calculus

    Sand pouring from a chute forms a conical pile whose height is always equal to the diameter. If the height increases at a constant rate of 5 ft/min, at what rate is sand pouring from the chute when the pile is 10 ft high?
  2. calculus

    Sand falls from a conveyor belt at a rate of 20 m^3/min onto the top of a conical pile. The height of the pile is always 3/4 of the base diameter. Answer the following. a.) How fast is the height changing when the pile is 10 m high?
  3. calculus

    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?
  4. CALCULUS

    A pile of sand in the shape of a cone whose base diameter is 4 times its height is being built up at 12 pi m3/min. How fast is the height of the pile increasing 3 min after the pouring begins.
  5. CALCULUS

    Sand is being poured from a converyer belt forming a conical pile whose base diameter is eual to its height at all times. If the base diameter is inreasing at 2 m/min when the base is 2 m wide. How fast is the sand being poured onto …
  6. 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?
  7. 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 …
  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. Calculus 1

    sand is being poured onto the ground forming a conical pile whose height equals 1/4 of the diameter of the base. The sand is falling at a rate of 20cm^3/sec. How fast is the height of the sand pile increasing when it is 3cm high?
  10. Calculus 1

    sand is being poured onto the ground forming a conical pile whose height equals 1/4 of the diameter of the base. The sand is falling at a rate of 20cm^3/sec. How fast is the height of the sand pile increasing when it is 3cm high?

More Similar Questions