Answer:
After 12 seconds, the area enclosed by the ripple will be increasing rapidly at the rate of 1206.528 ft²/sec
Explanation:
Area of a circle = πr²
where;
r is the circle radius
Differentiate the area with respect to time.
dr/dt = 4 ft/sec
after 12 seconds, the radius becomes =
To obtain how rapidly is the area enclosed by the ripple increasing after 12 seconds, we calculate dA/dt
dA/dt = 1206.528 ft²/sec
Therefore, after 12 seconds, the area enclosed by the ripple will be increasing rapidly at the rate of 1206.528 ft²/sec