(a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt.

Question

(a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt

 in terms of dr/dt.

dA/dt = ____ dr/dt

b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius is 39 m?

= ? m^2/s

Answer 1

a) Since A = π r², dA/dt = 2π r dr/dt.

b) If dr/dt = 1 m/s and r = 39 m, then dA/dt = 2π (39 m) (1 m/s) = 245 m²/s.