Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The area of the spill increases at a rate of 9π m²/min. How fast is the radius of the spill increasing when the radius is 10 m?

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Answer 1 · 2016-07-30T16:34:12

$dr|_(r=10)=0.45m//min$ .

Since area of a circle is $A=pi r^2$ , we may take the differential on each side to obtain :

$dA=2pirdr$

Hence the radius changes at the rate $dr=(dA)/(2pir)=(9pi)/(2pir)$

Thus, $dr|_(r=10)=9/(2xx10)=0.45m//min$ .