The area of a floating circular oil spill in the ocean is increasing at a rate of 96pi square meters per second. When the area of the spill is 1000pi how fast is the radius increasing in meters per second.

Answer 1

Area = πr^2
d(area)/dt = 2πr dr/dt

when area = 1000π
πr^2 = 1000π
r^2=1000
r = √1000 = 10√10

96π = 2π(10√10)dr/dt
dr/dt = 96/(20√10) or 24/(5√10) or 12√10/25
= appr. 1.52