On a hot summer day, you are trying to fill a small pool in your backyard to soak your feet. Water flows out of your garden hose and into the pool at a rate of 100 kg/min. However, your little brother has cut a hole in the bottom of your pool as a prank. The hole at the bottom is 3 cm, and water leaves with a velocity of 2 m/s. You notice that it takes you 20 minutes to change the level of the water by 0.3 m.
What is the diameter of your pool?