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