The graph above was obtained using the following model. The volume of a cone is V = πr2h/3.
For simplicity, let r = h, then V = πh3/3.
So the height of the cone is given by the cube root of 3V/π.
Example: A cone with h = r = 10 has volume 1000π/3 units.
If the water drains out in 10 seconds, it means 100π/3 units will drain out each second. Thus the amount of water left after t seconds is given by (1000 - 100t)π/3 units.
The height at time t will be the cube root of (1000 - 100t). This is the graph above.