Question

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?

Answer 1

The radius will increase at the rate of 0.64 mi/hr

Explanation:

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

Differentiating both sides w.r.t time

$\frac{dA}{dt}$ = 2π r $\frac{dr}{dt}$                                    II

Dividing II by I , we have

$\frac{dA}{A}$ = 2 x  $\frac{dr}{r}$

substituting the values

$\frac{dr}{r}$ = $\frac{5.5}{12}$ = 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