Math Is Fun Forum

Hey so i have set my differential equation as such:

A(h) = area of cross section of the water level in the tank at a given height (h)
a = area of the drain hole
h = height of tank at any given time
g = gravity

which forms the equation : A(h) * (dh/dt) = -a * root(2gh) .... describes how the height of the water level changes with time

My problem: a conical tank with a certain given height n radius i dripping water. I have been given the time that it takes for all the water to drain out of the tank and I have to find what the area of the drain hole has to be.

I know that i have to first find an expression for A(h) for the changing area of the cross section of water in the cone... and i dont know how I can relate the change of radius with the changing height...

please help? Thx