Calc 2: Volume Problem

Zaper

Joined Aug 17, 2010
43
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.

Zazoo

Joined Jul 27, 2011
114
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.