The Student Room Group

Connected rates of change - concentric circles

First the question:
At a given instant, the radii of two concentric circles are 8cm and 12cm.The radius of the outer cirlce is increasing at a rate of 1cm/second and the radius of the inner circle is increasing at a rate of 2cm/second. Find the rate of change of the area enclosed by the two circles.

I didn't really know what i was doing when i started this, i basically filled up some paper writing all i knew, working out rates of change of the area's of the circles with respect to time, and then realised that i didn't know how to relate them to each other in a general way.

I'd appreciate could point me in the right direction, i don't particularly want a worked solution, bear in mind i know how to work out connected rates of change, but this is too abstract for me to get my head around and figure out like the rest of them :frown:
Reply 1
Im not sure if this is right, but i'd first work out how the areas change over time (chain rule), then add the 2 rates together (this may be completely wrong but give it a try anyway)
Reply 2
I know this bumping an old thread, but i still can't do this question!
Reply 3
Does the question want the rate of change of the area inside the outer circle, but outside the inner circle? (i.e. between the two circles)

If so, just take the modulus of dA1dtdA2dt\frac{dA_1}{dt}-\frac{dA_2}{dt}

Where A1 and A2 are the areas of the circles
hmmm...
if A= area enclosed between the two circles then, and r (outer circle) and r' are the two radii

dr/dt=1
dr'/dt=2

A= πr^2-πr'^2

Differentiate above implicitly with respect to time, then put in the numbers to find the rate of change of area at the given instant.
Thats my stab at it anyway.