Let A(t) be the area of a circle with radius r(t), at time t in min. Suppose the radius is changing at the rate of drdt=6 ft/min. Find the rate of change of the area at the moment in time when r=9 ft

The rate of change is ft^(2)/min

Step-by-step explanation:

The area of a circle is given by the following equation:

To solve this question, we have to realize the implicit differentiation in function of t. We have two variables, A and r. So

We have that:

.

We want to find

So

Since the area is in square feet, the rate of change is in ft^(2)/min.

So the rate of change is ft^(2)/min

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