The problem is to find the area of the circular region covered by emitted pollutant that cannot rise vertically.

The pollutant begins emitting at 8:00am or t = 0 represents 8:00 am.

The radius of the circle of pollutants is r(t) = 2t miles.

A(r) = pi or 3.14r^2 that represents the area of a circle of radius r.

Find what the circular region would be by noon. I made t=4

then plugged it into the function.

A[r(t)] so I came up with

r(4) = 2(4) = 8 miles

then plug the 8 into the A function to be 3.14 * 8^2 = 200.96 miles. That can't be right, it is too many miles of coverage.

Where did I go wrong in my thinking?