Question

find the rate of change of the area of a circular disc with respect to its circumference when the radius is 3 cm 

Answer 1

The area of a circle is 

A = $\pi$*r^2 

Take the derivative with respect to time 

dA/dt = 2*$\pi$*r*dr/dt 

Substitute the appropriate values 

dA/dt = 2*$\pi$*2*3 = 12 $\pi$ $cm^{2}$/sec

Answer 2

circumference of circle 
C = 2*pi*r
dC/dt = 2*pi*dr/dt = k
area of circle
A = 2*pi*r²
dA/dt = 2*pi*2rdr/dt
dA/dt = 2*3*k = 6k