(a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt. dA dr dt dt (b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius is 23 m? m2/s Need Help? Read It

ach side of a square is increasing at a rate of 7 cm/s. At what rate is the area of the square increasing when the area of the square is 9 cm2?

An ant colony explores an area enclosed by a circle centered at its nest. This area (and the circle containing it) expands as they have time to explore. Due to the need for ants to return to the colony periodically, as the radius expands, the change in the radius of the area explored with respect to time slows down. Specifically, if r is the radius of the area the ants have explored in meters, then = 3 m/day. Find the rate of change of the area explored by the ants 4 in m2/day when the radius of the area explored is 3m. dt