What is the Radius When Area and Circumference Rates are Equal?

[DollarBill]

Homework Statement

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

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?

 

[HallsofIvy]

Homework Statement

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

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

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

So would the radius just be 1?

What was the question the problem asked?

 

[DollarBill]

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?

"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:"