A inverted conical vessel contains water to a height of 12cm initially. A hole is opened at the vertex and water leaks away in such a manner that after t minutes, the rate of decrease of the height, h cm, of the water in the vessel is given by dh/dt = -2t/3 cm/min

a) calculate the time taken for the vessel to empty

b)Given the volume of water in the vessel after t minutes is ( h^3) cm^3 , calculate the rate of change of the volume of water in the vessel when t =3

I am already stumped by the first part. As dh/dt is constantly changing due to the vessel not being uniform in base area as the water level decreases i can't just divide the figures. Can anyone point me in the right direction for this question?