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.