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# C4 connected rates of change watch

1. I'm having a bit of trouble with this 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.

Basically I've got my area as (pi)r^2 of the outer circle minus (pi)r^2 of the inner circle, which gives me dA/dr of 8pi when i differentiate and put in my r values (since dA/dr = 2(pi)r).

since dA/dt = dA/dr x dr/dt i multiplied by both 2 and 1 from my 2 dr/dt values which gives me 16pi which is obviously wrong.

Does that mean that I'm only supposed to multiply by the dr/dt of the outer circle? If so, why is that? Thanks a lot, sorry this is a bit long to read!
2. (Original post by Killyouraorta)
Basically I've got my area as 2(pi)r^2 of the outer circle minus 2(pi)r^2 of the inner circle, which gives me dA/dr of 8pi when i differentiate and put in my r values (since dA/dr = 2(pi)r).
Huh? Isn't the area of a circle ?
3. (Original post by Zacken)
Huh? Isn't the area of a circle ?
My bad, thats what I meant!

i think i worked it out, i had to do everything for the outer circle and inner circle separately and then minus it out
4. (Original post by Killyouraorta)
My bad, thats what I meant!

i think i worked it out, i had to do everything for the outer circle and inner circle separately and then minus it out
Ah, okay - yeah, that's a good approach! Good job.
5. (Original post by Zacken)
Ah, okay - yeah, that's a good approach! Good job.
Thank you!

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