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 increasing when the pile is 25 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is given by V=(π/3)(r^2)h

  1. 👍 4
  2. 👎 1
  3. 👁 3,268
  1. V=(π/3)(r^2)h
    but we are told that h = 2r or r = h/2

    V = (1/3)π (h/2)^2 (h) = (1/3)π h^3/4
    =(1/12)π h^3
    dV/dt = (1/4)π h^2 dh/dt

    10 = (1/4)π(625) dh/dt
    dh/dt = ....

    you finish it.

    1. 👍 3
    2. 👎 26

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    A moving conveyor is built to rise 4 ft for each 5 ft of horizontal change. Suppose the conveyor runs between two floors in a factory. Find the length of the conveyor if the vertical distance between floors is 8 feet. (Round your

  2. math

    What is the volume of the box pictured below? A rectangular prism of length 3 and 1 over 2 feet, width 3 and 1 over 8 feet, and height 4 over 5 foot is shown. fraction 3 and 1 over 10 cubic feet fraction 3 and 2 over 5 cubic feet

  3. Physics

    A 20 kg crate is placed on a horizontal conveyor belt. The materials are such that us = 0.47 and uk = 0.21. What is the maximum acceleration the belt can have without the crate slipping? If acceleration of the belt exceeds the

  4. 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

  1. MATH

    A contractor purchases gravel one cubic yard at a time. (a) A gravel driveway L yards long and 6 yards wide is to be poured to a depth of 1 foot. Find a formula for n(L), the number of cubic yards of gravel the contractor buys,

  2. Physics

    A 0.075 kg ball in a kinetic sculpture moves at a constant speed along a motorized conveyor belt. The ball rises 1.32 m above the ground. A constant frictional force of 0.350 N acts in the direction opposite the conveyor belt's

  3. Physics

    Dana loads luggage into an airplane using a conveyor belt tilted at an angle of 20°.She places a few pieces of luggage on the belt before it starts to move, then she turns the belt on. It takes the belt 0.70 s to reach its top

  4. physics

    A conveyor belt is moving grain into a bin that is 3.20 m below the top of the conveyor belt. The grain does not slip on the conveyor belt that is inclined at 15.0° and they move at a constant speed of 6.00 m/s. In order for the

  1. Physics

    A piece of luggage is being loaded onto an airplane by way of an inclined conveyor belt. The bag, which has a mass of 10.0 kg, travels 6.50 m up the conveyor belt at a constant speed without slipping. If the conveyor belt is

  2. Physics

    Boxes are moved on a conveyor belt from where they are filled to the packing station 11.3m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for

  3. 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

  4. physics

    A conveyor belt is moving grain into a bin that is 1.90 m below the top of the conveyor belt. The grain does not slip on the conveyor belt that is inclined at 15.0° and they move at a constant speed of 6.00 m/s. In order for the

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