The radius of a circle is increasing at a constant rate of 0.2 meters per second. what is the rate increase in the area of the circle at the instant when the circumference of the circle is 20π meters? v

Area of a circle, A = πr^2

Therefore,

dA/dt = 2πr. dr/dt, but dr/dt = 0.2

Additionally,

Circumference of a circle, C = 2πr

Then, at C = 20π;

20π = 2πr = > r = 20π/2π = 10

At C = 20π;

dA/dt = 2πr. dr/dt = 2π*10*0.2 = 4π m^2/s