Do you know the formula for area of a circle?
The rate of change of the area is the derivative of that.
Basketball players will often say that the hoop seems to get bigger as they get “hot” during a game. A basketball hoop is a metal circle with a diameter of 18”. In a recent game, Leandro Barbosa got “hot”, hitting three point shots one after another. Leandro “saw” the hoop’s diameter grow half an inch per minute during his hot streak. At what rate is the area of the hoop changing after 4 minutes?