>a swimming pool is being filled
>the height of the water level of the pool determines at how many liters per minute the tap is pouring water into the pool (for example, when the water level is at 4.7 mark, the water is coming at 4.7 liters per minute)
>at the bottom the water flow is one liter per minute (the flow rate starts as this when the pool is empty) and at the very top it is going to be 11 liters per minute.
>in other words, we can conclude that when the height of the water level is X times the pool radius, the water flow is 10X+1 liters per minute
>to makes matters more complicated, the pool is shaped as a hemisphere
>the radius of the hemisphere is three meters
How long does is take to fill the pool entirely?