Oil leaks out from a damaged oil tanker and forms a circle around the tanker. If the radius of the circle of oil is increasing at 25m/min, find the rate of change of the area when the radius is 20km

Answer 1

A = πr^2
dA/dt = 2πr dr/dt
when r = 20000 m , dr/dt = 25 m/min

dA/dt = 2π(20000)(25) = 1,000,000π m^2/min
= π km^2/min

(1 km = 1000 m
1 km^2 = (1000)^2 or 1,000,000 m^2)