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

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SUMMARY

The discussion focuses on calculating the rate of growth of the radius of a leaking oil patch with an area increasing at 250 square meters per hour. The area of the patch is given as 1900 square meters. The correct approach involves using the formula for the area of a circle, A = πr², to find the radius and then applying the relationship dr/dt = dA/dt / (2πr) to determine the rate of change of the radius. The final answer should be expressed to two significant figures.

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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
 
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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.
 
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
 

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