Answer:
[tex]-0.2Cmm/sec[/tex]
Step-by-step explanation:
List given and unknown information
[tex]\frac{dr}{dt}=-0.2mm/sec\\ \\\frac{dA}{dt}=?\\ \\A=\pi r^2\\\\C=2\pi r[/tex]
Differentiate area with respect to time and make proper substitutions
[tex]A=\pi r^2\\\\\frac{dA}{dt}=2\pi r\frac{dr}{dt}\\ \\\frac{dA}{dt}=C(-0.2)\\ \\\frac{dA}{dt}=-0.2C[/tex]
Therefore, the rate of change of the area of the circle, in terms of the circumference, C, is [tex]-0.2Cmm/sec[/tex]
