Question

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 2 m/s. How fast is the area of the spill increasing when the radius is 19 m?

Answer 1

This is a very simple problem:
\[A=\pi r^2\]
And you know that the change in radius dr/dt = 2 m/s

Answer 2

Now you have to find out what dA/dt is, when r = 19m
To find this, take the derivative of Area:
dA/dt = 2*pi*r*(dr/dt)

Answer 3

You need to know what is the change in area when r =19m and dr/dt = 2m/s so plug those values in:
dA/dt = 2pi * 19m * 2m/s
dA/dt = 76*pi (m^2/s) <=Your answer

Answer 4

looks good , i concur