Calculus

posted by .

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 m deep.

  • Calculus -

    let the height of the water be h m
    let the radius of the water be r m
    by ratios : h/r = 5/3
    5r = 3h
    r = 3h/5

    Volume = (1/3)π r^2 h
    = (1/3)π(9h^2/25)h
    = (3π/25)h^3
    d(Volume)/dt = (9π/25)h^2 dh/dt
    2 = (9π/25)(9)dh/dt
    dh/dt = 50/(81π) m/s

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    Water is leaking out of an inverted conical tank at a rate of 11400 cm^3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 8.0m and the the diameter at the top is 3.5m. If the water …
  2. Calculus

    Water is leaking out of an inverted conical tank at a rate of 10,000 cm^3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6m and the diameter at the top is 4m. If the water level …
  3. calculus

    Water is leaking out of an inverted conical tank at a rate of 10,000 cm^3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level …
  4. 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 …
  5. 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 …
  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. Calculus 1

    Water is leaking out of an inverted conical tank at a rate of 12,000 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level …
  8. math

    Water is leaking out of an inverted conical tank at a rate of 10600.0 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 14.0 m and the the diameter at the top is 6.0 m. If the …
  9. Calculus 1

    Water is leaking out of an inverted conical tank at a rate of 9,500 cm^3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level …
  10. Calculus - Rates of Change

    A water tank has a shape of an inverted cone with a base radius of 2m and a height of 4 m. If water is being pumped into the tank at a rate of 2m3/min, then find the rate at which the water level is rising when the water is 3m deep. …

More Similar Questions