Answer to Question #248145 in Calculus for kae

Question #248145

The radius of a circular oil slick on the surface of a pond is increasing at the rate of 10 meters/min. At what rate is the circle's area changing when the radius of the oil slick is 20 m. ?


1
Expert's answer
2021-10-08T08:02:40-0400

Given

"\\frac{dr}{dt}=10 m\/min"

We have to find "\\frac{dA}{dt}" at r=20 metrs

Now "A=\u03c0r^2"

"\\frac{dA}{dt}=2\u03c0r\\frac{dr}{dt}"

At r=20m

"\\frac{dA}{dt}=2\u03c0 \\times 20 \\times 10=400\u03c0 \\\\\n\n\\frac{dA}{dt}=1256"


Answer 1256 m/min



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