How to find the radius when the area and circumference are changing at the same rate

The video tutorial discusses the problem of an expanding circle, focusing on the relationship between the rate of increase in the area and the circumference. It explains how to derive expressions for these rates and solve for the radius when the rates are numerically equal. The tutorial emphasizes understanding the mathematical process and correctly applying derivatives with respect to time.

What does it mean when the text states that the rate of increase in the area is numerically equal to the rate of increase in the circumference?

If the radius of the circle is 1, what would be the area and circumference?