Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 5.5 mi2/hr. How rapidly is radius of the spill increasing when the area is 6 mi2?

Explanation:

The area of a circle can be represented by  A = π r²            I

Differentiating both sides w.r.t time

= 2π r                                    II

Dividing II by I , we have

= 2 x  

substituting the values

= = 0.46 mi per unit radius

or dr = 1.4 x 0.46 = 0.64 mi/hr

here 1.4 mi is the radius , when area of circle is 6 mi²

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