calculus

posted by .

6. A parabaloid with height h and radius r has volume 1/2 pieR^2H. Consider a parabaloid-shaped water
tank with height of 7m and radius of 4m. If V is the volme of water in the tank and h is the depth
of water,
find the relationship between dV/dt and dhdt.
How is the volume changing when h = 3m and
dh/dt = 0.2m/s?

  • calculus -

    dV/dt = surface area * dh/dt (geometry , no calculus really required, draw picture)
    dV/dt = pi r^2 dh/dt

  • calculus -

    consider a cross-section of the paraboloid placed with vertex at the origin an opening upwards
    then its equation would be
    y = ax^2
    when x=4, y = 7
    y = (7/16)x^2
    or
    h = (7/16)r^2 , using r and h
    r^2 = 16h/7

    V = (1/2)πr^2h
    = (1/2)π(16h/7)h
    = (8π/7) h^2
    dV/dt = 16π/7 h dh/dt ----> the relationship between dV/dt and dh/dt

    Whe h=3 and dh/dt = .2

    dV/dt = (16π/7)(3)(.2) = ......

    I will let you do the button pushing.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math - Calculus 2

    An underground tank full of water has the following shape: Hemisphere - 5 m radius. at the bottom Cylinder - radius 5 m and height 10m in the middle Circular cone radius 5 m and height 4 m at the top The top of the tank is 2 m below …
  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

    A water tank is shaped like an inverted right circular cone with a base radius of 14 feet and a height of 25 feet high. If water flows into the tank at a rate of 20 ft^3/min, how fast is the depth of the water increasing when the water …
  4. Calculus I

    *Optimization problem* [I don't know how to get to the answer] Problem: You have a cylindrical can with radius 4cm and height 10cm. Inside is a marble with a radius that has to be larger than 0 but less than 4 cm (even the largest …
  5. Calculus

    Water is draining at a rate of 2 cubic feet per minute from the bottom of a conically shaped storage tank of overall height 6 feet and radius 2 feet . How fast is the height of water in the tank changing when 8 cubic feet of water …
  6. Algebra

    a cylindrical water tank has a volume of 20π cubic feet . the height of the tank is 1 foot more than 2 times of its radius . find the radius and height of the tank
  7. Calculus

    A cylindrical water tank has radius r=1 meter and height 10 meters. Suppose the tank is lying on its side and is filled halfway with water. How much work does it take to pump all the water out the top of the tank?
  8. Calculus

    Water is draining from a small cylindrical tank into a larger one below it. The small cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a radius of 8 feet and a height of 16 feet. The small …
  9. CALCULUS

    Water is draining from a small cylindrical tank into a larger one below it. The small cylindrical tank has a radius of 4 feet and a height of 6 feet; the large cylindrical tank has a radius of 8 feet and a height of 16 feet. The small …
  10. Calculus AB

    Water pours at a constant rate into a conical tank of height 10 feet and radius 4 feet. Let V, h and r be the volume, height, and radius if the water in the tank at a particular time t. Express the volume of the water in the tank at …

More Similar Questions