Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 3 mi^2/hr. How rapidly is the radius of the spill increasing when the area is 6 mi^2?

Question

Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 3 mi^2/hr. How rapidly is the radius of the spill increasing when the area is 6 mi^2?

Find the equation of the area in terms of t.

Note that A = πr^2

A(t) = ? mi^2

Answer 1

Relation of A to radius: A = πr²

Take derivative wrt time:

dA/dt = 2πrdr/dt

dr/dt = (dA/dt)/(2πr)

You can substitute in all the values on the right-hand-side (Note that r = sqrt(6/π) from πr² = 6

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