Find the Rate of Growth of a Leaking Oil Patch at 1900 Square Metres

[Maatttt0]

Homework Statement

Leaking oil is forming a circular patch on the surface of the sea. The area of the patch is
increasing at a rate of 250 square metres per hour. Find the rate at which the radius of the patch
is increasing at the instant when the area of the patch is 1900 square metres. Give your answer
correct to 2 significant figures.

Homework Equations

The Attempt at a Solution

dA/dr = 2πr ... dA/dt = 250

therefore dr/dt = 250/2πr

I've tried 250/2πr = 1900 to find r but that doesn't seem to be correct :\

I'm not sure what I'm missing - please help, thanks

 

[hgfalling]

Well, yes, it wouldn't be correct for you to set dr/dt (the rate at which the radius is increasing per time) equal to 1900 (the size of the patch at some point in time).

You want the rate at which the radius is increasing when the area is 1900. You have an expression for the rate. So evaluate that expression.

 

[Maatttt0]

Ahh got it thank you

Integrate the dA/dt to get πr^2 and work out r by equating it to the 1900 then sub the r back into the dr/dt, thanks