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. 👍 0
  2. 👎 0
  3. 👁 1,046
  1. h = 2r, so

    v = 1/3 pi r^2 * 2r = 2pi/3 r^3

    dv/dt = 2pi r^2 dr/dt
    10 = 2pi*4^2 = 32pi dr/dt
    dr/dt = 5/16pi

    now, c = 2pi*r, so
    dc/dt = 2pi dr/dt
    = 2pi * 5/16pi = 10/16 = 5/8

    1. 👍 1
    2. 👎 0
  2. Pauline jogs at 5 1/3 miles per hour for 1 5/6 hours. about how many miles has she walked?

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. 7th Grade Proportion Help

    A 10 acre field produced 750 bushels of corn. At that rate, how much corn can be produced from a 14-acre field? I really need help understanding this question I'm not looking for the answer. Please Help Me!

  2. thermodynamics

    if a pump discharges 75 gpm of water whose specific weight is 61.5 lb/ft^3(g=31.95fps^2). find a) the mass flow rate in lb/min, and b) and total time required to fill a vertical cylinder tank 10ft in diameter and 12ft high.

  3. Calculus

    The base of a triangle is shrinking at a rate of 1 cm/min and the height of the triangle is increasing at a rate of 6 cm/min. Find the rate (in cm2/min) at which the area of the triangle changes when the height is 38 cm and the

  4. physics

    An 8.00kg package in a mail-sorting room slides 2.00 m down a chute that is inclined at 53.0 degrees below the horizontal. The coefficient of kinetic friction between the package and the chute's surface is 0.400. Calculate the

  1. Calculus

    A container in the form of a right circular cone (vertex down) has a radius of 4m and height of 16m. If water is poured into the container at the constant rate of 16m^3/min, how fast is the water level rising when the water is 8m

  2. calculus

    Water is poured into a conical tank 6m across the top and 8m deep at the rate of 10m/min. How fast is the water level rising when the water in the tank is 5m deep?

  3. Math

    a man 6ft tall walks at the rate of 5ft/sec toward a streetlight that is 16ft above the ground. At what rate is the length of his shadow changing when he is 10ft from the base of the light?

  4. related rates with work shown

    this is a relate rates problem in calculus in a right triangle, the hypotenuse is 5 and the vertical side is x and the angle is theta. so if theta increases at a constant rate of 3 radians per minute, at what rate is x increasing

  1. 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

  2. algebra 2

    A skydiver jumps from an airplane at an altitude of 2,500 ft. He falls under the force of gravity until he opens his parachute at an altitude of 1,000 ft. Approximately how long does the jumper fall before he opens his chute?

  3. Math -Trig Please help!

    At one time, Maple Leaf Village (which no longer exists) had North America’s largest Ferris wheel. The Ferris wheel had a diameter of 56 m, and one revolution took 2.5 min to complete. Riders could see Niagara Falls if they were

  4. 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? Volume of a

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