In a trend that scientists attribute, at least in part, to global warming, a certain floating cap of sea ice has been shrinking since 1980. The ice cap always shrinks in the summer and grows in winter. Average minimum size of the ice cap, in square miles, can be approximated by $A=\pi r^{2}$. In 2013 , the radius of the ice cap was approximately $759 \mathrm{mi}$ and was shrinking at a rate of approximately $4.8 \mathrm{mi} / \mathrm{yr}$. How fast was the area changing at that time? The area was changing at a rate of in 2013. (Round to the nearest integer as needed.)

Step 1 ：We are given that the area of the ice cap is given by the formula \(A=\pi r^{2}\), and the radius is shrinking at a rate of \(4.8 \mathrm{mi} / \mathrm{yr}\).

Step 2 ：We can use the chain rule to find the derivative of the area with respect to time, which will give us the rate of change of the area.

Step 3 ：The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Step 4 ：In this case, the outer function is \(A=\pi r^{2}\) and the inner function is \(r\), which is changing with respect to time.

Step 5 ：So, we need to find the derivative of \(A\) with respect to \(r\), and then multiply that by the derivative of \(r\) with respect to time.

Step 6 ：Given that \(r = r\) and \(dr/dt = -4.8\), we find that \(A = \pi r^{2}\) and \(dA/dr = 2\pi r\).

Step 7 ：Then, we find that \(dA/dt = -9.6\pi r\) and \(dA/dt_{2013} = -22891\).

Step 8 ：Final Answer: The area of the ice cap was changing at a rate of approximately \(\boxed{-22891}\) square miles per year in 2013.