Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 9 mi2/hr. How rapidly is radius of the spill increasing when the area is 4 mi2?

Answer 1

a = πr^2
when a=4, r=2/√π
da/dt = 2πr dr/dt
9 = 2π(2/√π) dr/dt
dr/dt = 9/(4√π) mi/hr