The Area of a circle increases at a rate of 1 cm^2/s. How fast is the radius changing when the circumference is 2 cm?

Question

anonymous · Answer

This is a related rates question. Do you know the first step to tackling these?

anonymous · Answer

Yes. But i dont know how to apply the formulas

anonymous · Answer

A=pi r^2 and C=2pi r

anonymous · Answer

Ok, and they give you the rate at which it is increasing this is the differential dA/dt=1

anonymous · Answer

i dont get how you can find all the variables

anonymous · Answer

And now we need to find the radius first off to plug it into our final formula. 
Alright we know that C=2 pi r and they tell us our C is 2 so it will become

$$\Large 2=2\pi~r$$

Solve for r first off

anonymous · Answer

r= 2/2pi

anonymous · Answer

Alright and that simplifies to 1/pi now we can move on to differentiate the Area (since that's what we're working with) and find it with respect to t (time) do you know how to do that? It's kind of like implicit differentiation with the circle equation 
$$\Huge x^2+y^2=r^2$$
where r is the radius and would be a constant.

anonymous · Answer

differentiate the equation?

anonymous · Answer

where did this eqtn come from ?

anonymous · Answer

but i think its 2x dx/dt +2y dy/dt = 1/pi^2

anonymous · Answer

No, no sorry I was just referecning to this equation

anonymous · Answer

I just meant for the area formula can you implicitly differentiate which I see you can and so we'd have 

$$\Huge A=\pi~r^2$$

and we need to differentiate with respect to (time) and sorr @Jennings15  my computer restarted

anonymous · Answer

its ok

anonymous · Answer

dA/dt = 2pi r dr/dt

anonymous · Answer

r=1/pi

anonymous · Answer

Ok and the question is asking for how fast the radius is chaning, the rate of change of the radius (dr/dt)

We know dA/dt to be 1 since they gave it to us (1cm^2) and we know r to be 1/pi so we just plug in and solve for dr/dt

anonymous · Answer

1cm^2/s *

anonymous · Answer

omg wow man . thats freaking amazing. let me solve this nw

anonymous · Answer

1=2pi/pi dr/dt
1=2dr/dt
1/2=dr/dt

anonymous · Answer

Anytime, I remember these, let me guess you're in Calc AB or some type of calculus class?

anonymous · Answer

preciate it bro , and yeah im in calculus/analytic gemotery 1 .

anonymous · Answer

And that looks about right, make sure to put your answer in the correct units so it's a length so it would just be 1.2cm/s

anonymous · Answer

1/2 cm/s*