A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of 4 feet per minute. Find the rate at which the area is changing at the instant the radius is 11 feet. When the radius is 11feet, the area is changing at approximately square feet per minute. (round to the nearest thousandth)

When the radius is 11 feet, the area is changing at approximately 276.571 square feet per minute.

Step-by-step explanation:

We are given the following in the question:

Instant radius = 11 feet

Area of circle =

where r is the radius of the circle.

Rate of change of area of circle =

Putting all the values, we get,

Thus, when the radius is 11 feet, the area is changing at approximately 276.571 square feet per minute.