1. Oct 18, 2008

### DollarBill

1. The problem statement, all variables and given/known data
The radius of a circle is increasing at a nonzero rate, and at a certain instant, the rate of increase in the area of the circle is numerically equal to the rate of increase in its circumference

3. The attempt at a solution
c=circumference
a=area

If the rate of change in the circumference and area are equal,

da/dt = dc/dt

πr2=2πr

2πr da/dt = 2π dc/dt

So would the radius just be 1?

2. Oct 18, 2008

### HallsofIvy

Staff Emeritus
This is incorrect. Since you have converted from a and c to functions of r, the derivatives are both dr/dt: $2\pi r dr/dt= 2\pi dr/dt$

What was the question the problem asked?

3. Oct 18, 2008

### DollarBill

"The radius of a circle is increasing at a nonzero rate, and at a certain instant, the rate of increase in the area of the circle is numerically equal to the rate of increase in its circumference. At this instant, the radius of the circle is:"