Question

The radius of a circular puddle is growing at a rate of 15 cm/s.

(a) How fast is its area growing at the instant when the radius is 30 cm?


(b) How fast is the area growing at the instant when it equals 49 cm2?

Answer 1

A= pi*r^2

can you differentiate that with respect to time?

Answer 2

A and r are both functions of time, so use implicit differentiation... try it and let me know what you get...

Answer 3

For the second one I set dr/dt = (15)(2pi(49/pi)^.5) and got the right answer. I'm trying to figure out how to know the area when it's cm instead of cm^2 they're asking for (like the first part; a). I'm lost in my own math.

Answer 4

(b) is asking for dA/dt...

Answer 5

dA/dt = 2 pi r dr/dt

when A= 49 r = (49/pi)^.5 ... so that part is right... and the 15 is right for dr/dt

I guess you just accidentally wrote 'dr/dt' when you meant 'dA/dt'

Answer 6

Is it that you're having trouble with the first part of the question?

Answer 7

dA/dt = 2 pi (30) * 15

Answer 8

I am just doing my arithmetic wrong it looks like, but thanks so much for your help and investigating!