Calculus

posted by .

A container is in the shape of an inverted right circular cone has a radius of 2 in at the top and a height of 6 in. At the instant when the water in the conatiner is 5 in deep, the surface level is falling at the rate of -.4 in/s. Find the rate at which the water is being drained.

  • Calculus -

    when the water is at height x, by similar triangles, the radius r of the surface is given by

    r/x = 2/6, so r = x/3

    v = 1/3 pi (x/3)^2 * x
    = pi/27 x^3

    dv/dt = 2pi/27 x^2 dx/dt
    -4 = 2pi/27 (25) dx/dt

    dx/dt = -54/25pi = -.69 in/s

  • Calculus - correction -

    dv/dt = 3pi/27 x^2 dx/dt
    -4 = pi/9 (25) dx/dt

    dx/dt = -36/25pi = -.46 in/s

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    A water tank has a shape of an inverted circular cone with base radius 3 m and height of 5 m. If the water is being pumped into the tank at a rate of 2 m^3 /min, find the rate at which the water level is rising when the water is 3 …
  2. Calculus - free body diagram

    A water tank has the shape of an inverted right circular cone whose base radius is equal to half its height. Water is being pumped in at 2 cubic meters per second. How fast is the water rising when the water is 3 meters deep?
  3. math

    Suppose we pump water into an inverted right-circular cone tank at the rate of 6 cubic feet per minute. The tank has the height 9 ft and radius on the top is 8 ft. What is the rate at which the water level is rising when the water …
  4. Calculus

    A vessel is in the shape of an inverted cone. The radius of the top is 5cm and the height is 8cm. Water is poured into a height of xcm. Show that if the volume of the water is Vcm^3,then V=(25/192)*pi*x^3. (The volume of a cone is …
  5. Pure Maths

    A container is in the shape of a right circular cone (inverted) with both height and diameter 2 meters. It is being filled with water at a rate of (pi)m^3 per minute. Fine the rate of change of height h of water when the container …
  6. Calculus

    A large container has the shape of a frustum of a cone with top radius 5 m, bottom radius 3m, and height 12m. The container is being filled with water at the constant rate 4.9 m^3/min. At what rate is the level of water rising at the …
  7. calculus

    A large container has the shape of a frustum of a cone with top radius 5 m, bottom radius 3m, and height 12m. The container is being filled with water at the constant rate 4.9 m^3/min. At what rate is the level of water rising at the …
  8. Calculus

    A large container has the shape of a frustum of a cone with top radius 5m, bottom radius 3m, height 12m. The container is being filled with water at the constant rate of 3.9 m^3/min. At what rate is the level of water rising at the …
  9. calculus inverted cone

    A container in the shape of an inverted cone has radius 6 ft and height 12 ft. It is being drained at 2〖ft〗^3/min. Find the rate of change of the height of the liquid in the cone when the height is 3 feet. The ratio of …
  10. Calculus

    Along reservoir has the shape of a right circular cone having a radius of 40m at the top and a height of 10m at the centre. it is being filled at a constant rate of 40 m^3/min.Find the rate at which the water level is rising when the …

More Similar Questions