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The radius of a circle is decreasing at a constant rate of 0.2 mm/sec. In terms of the circumference, C, what is the rate of change of the area of the circle in mm2/sec

Sagot :

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]

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