The solution would be like this for this specific problem:
Given:
Oil spill radius constant rate increase = 1 m/s
r = 34m
Let the area of the spill
be A and then let its radius be r.
Then A = π r².
Differentiating with
respect to t:
dA / dt = 2π r dr / dt.
Substituting r = 34 and dr / dt = 1:
dA/dt = 2 π * r * dr / dt
dA/dt = 2π * 34 * 1 = 68π = 214 m²/s, to 3 significant figures.
So, given that the radius is 34m, then the area of the spill is increasing at 214 m²/s.
