(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

area-of-a-circle

#1

(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.
(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 30 m?

Answer:

(a)
A= πr^2
dA/dt = 2π
r*(dr/dt)

(b)
rate of area (dA/dt) when r = 30 m
relationship: A = πr^2
so dA/dt = 2πr(dr/dt) from part a
dA/dt = 2π(30)(1)
= 60π m^2/s