Calculus

sand is falling into a conical pile so that the radius of the base of the pile is always equal to one half its altitude. of the sand is falling at the rate of 10 cubic feet per minute, how fast is the altitude of the pile increasing when the pile is 5 feet deep?

  1. 👍 1
  2. 👎 0
  3. 👁 2,839
  1. given: r = h/2

    V = (1/3)π r^2 h
    = (1/3)π (h/2)^2 (h)
    = (1/12) π h^3

    dV/dt = (1/4)π h^2 dh/dt
    for the given data ...

    10 = (1/4)π(25)dh/dt
    dh/dt = 10(4)/((25π) = 1.6/π feet/min

    check my arithmetic

    1. 👍 1
    2. 👎 2
  2. hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Related Rates

    Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. 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

  2. Related Rates

    Sand is falling into a conical pile at the rate of 10 m3/sec such that the height of the pile is always half the diameter of the base of the pile. Find the rate at which the height of the pile is changing when the pile is 5 m.

  3. 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

  4. Related rates

    Sand is being dropped at the rate of 10 cubic meter per minute onto a conical pile. If the height of the pile is always twice the base radius, at what rate is the height increasing when the pile is 8 meters high?

  1. calculus

    At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at the rate of 10 cubic feet per minute. The diameter of the base of the cone is approx­ imately three times the altitude. At what rate is the

  2. Calculus - Rate of Change

    Can someone explain how to solve this problem? Sand is being dumped on a conveyor belt onto a pile in such a way that the pile forms in the shape of a cone whose radius is always equal to its height. Assuming that the sand is

  3. calculus

    Sand is poured at the rate of 10 m cube /min so as to form a conical pile whose altitude is always equal to the radius of its base a) How fast is the radius increasing when it is 5 meters? b) Find the rate at which the area of its

  4. 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? Please explain

  1. Calc

    Gravel is being dumped from a conveyor belt at a rate of 10 ft^3/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

  2. calculus

    sand is being dropped onto a conical pile in such a way that the height of the pile is always twice the base radius.what is the rate of change of the volume of the pile with respect to the radius when the radius of the pile is 12

  3. 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?

  4. Calculus

    Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile

You can view more similar questions or ask a new question.