Question

The area of a circular oil slick is increasing at a constant rate of 2 square miles per day. How fast is the radius increasing when the area is 4(pi) square miles (approximately 12.57 square miles)?

So far I have that the area increases at the rate of x+(2mi^2/d) but I don't think that's right

Answer 1

a = πr^2
da/dt = 2πr dr/dt

So, plug in your numbers. When a = 4π, r=2, so

2 = 2π*2 dr/dt
dr/dt = 1/(2π) miles/day