Calc 2: Volume Problem

Discussion in 'Math' started by Zaper, Jan 13, 2012.

  1. Zaper

    Thread Starter Member

    Aug 17, 2010
    43
    0
    I'm having trouble figuring this Calc 2 problem given to me in class:

    A water tank is obtained by revolving the curve y=kx^4, k>0, about the y axis.

    a) Find V(y), the volume of water in the tank as a function of its depth, y.

    b) Water drains through a small hole according to Torricelli's law:
    (dV/dt = -m√y). Show that the water level falls at a constant rate.

    For part a I solved the equation for x, squared this and multiplied by ∏, and finally integrated to get: V=(2∏/3√k)*(y^3/2). I think that this is correct, but if not could someone show me where I went wrong?

    Also I am stumped as to how to go about part b so any help with that would be much appreciated.
     
  2. Zazoo

    Member

    Jul 27, 2011
    114
    43
    I'm not able to check your solution right now as I'm not near pen/paper, but your process looks good (i.e. disks of height dy)

    For part b, you found the function that relates the water level, y, to the volume of water, V, in part a. Taking the derivative of this function and setting it equal to the RHS of Torricelli's will then allow you to solve for dy/dt, which should be a constant.
     
  3. Zaper

    Thread Starter Member

    Aug 17, 2010
    43
    0
    Thank you. I worked it out how you said and it worked out for me as far as I can tell.
     
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