Calculus - free body diagram

posted by .

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?

  • Calculus - free body diagram -

    radius = (1/2)h
    r = (1/2)h
    r = h/2

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

    when h = 3, dV/dt = 2
    2 = (1/4)π(9) dh/dt
    dh/dt = 8/(9π) m/s

    Check my calculations, I did not write them out first.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Water is being pumped into an inverted conical tank at a constant rate. The tank has height 9 meters and the diameter at the top is 4 meters. If the water level is rising at a rate of 28 centimeters per minute when the height of the …
  2. 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 …
  3. Calculus (pleas help!!!)

    Water is leaking out of an inverted conical tank at a rate of 1100.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 15.0 meters and the diameter at the top …
  4. calculus - please help!

    Water is leaking out of an inverted conical tank at a rate of 13200 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 9 meters and the diameter at the top is …
  5. Calculus (Help please)

    A tank has the shape of an inverted circular cone with a base radius of 5 meters and a height of 20 meters. If water is being pumped into the tank at 2 cubic meters per minute, find the rate at which the water level is rising when …
  6. Math (Calculus)

    A tank has the shape of an inverted circular cone with a base radius of 5 meters and a height of 20 meters. If water is being pumped into the tank at 2 cubic meters per minute, find the rate at which the water level is rising when …
  7. Math (Calculus)

    A tank has the shape of an inverted circular cone with a base radius of 5 meters and a height of 20 meters. If water is being pumped into the tank at 2 cubic meters per minute, find the rate at which the water level is rising when …
  8. Steve and Reiny

    A tank has the shape of an inverted circular cone with a base radius of 5 meters and a height of 20 meters. If water is being pumped into the tank at 2 cubic meters per minute, find the rate at which the water level is rising when …
  9. calculus

    A water tank has the shape of an inverted right circular cone with base radius 3 meters and height 6 meters. Water is being pumped into the tank at the rate of 12 meters3/sec. Find the rate, in meters/sec, at which the water level …
  10. physics

    Water is leaking out of an inverted conical tank at a rate of 10700.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 7.0 meters and the diameter at the top …

More Similar Questions