How fast is the circumference changing when .....

[eddy2017]

Hi, dear friends and teachers:
Chris and Jake are cooking pancakes. Jake ladles the pancake batter into the frying pan. While the pancakes cooks the radius of the circular pancakes formed increases at a rate of 1 cm per minute. How fast is the circumference changing when the radius is 7 cm?.
As always, appreciating any insight into the solution of my problems.
eddy

 

[Romsek]

[MATH]c = 2\pi r\\ \dfrac{dc}{dt} = 2\pi \dfrac{dr}{dt}[/MATH]
I leave you to complete it. Ask yourself whether the current pancake radius affects the rate of the circumference growth.

 

[eddy2017]

Use implicit differentiation.

[MATH]c = 2\pi r\\ \dfrac{dc}{dt} = 2\pi \dfrac{dr}{dt}[/MATH]
I leave you to complete it. Ask yourself whether the current pancake radius affects the rate of the circumference growth.

Thanks, let me have a try.

 

[eddy2017]

Thanks, let me have a try.

I am on it. It will take me some time. This is something new for me.

 

[eddy2017]

Thanks, let me have a try.

I am so sorry. I thought the solution was easier. I started studying something about explicit and implicit differentiation, but this is something that I am not even familiar with. I will have to put his on hold until I get more knowledge about derivatives. It is something that i have not studied yet. Thanks a lot for your help, notwithstanding.

 

[Romsek]

I am so sorry. I thought the solution was easier. I started studying something about explicit and implicit differentiation, but this is something that I am not even familiar with. I will have to put his on hold until I get more knowledge about derivatives. It is something that i have not studied yet. Thanks a lot for your help, notwithstanding.

Forget I ever mentioned implicit differentiation and just start at post #2.

It's not that hard. You can do it!

 

[eddy2017]

Forget I ever mentioned implicit differentiation and just start at post #2.

It's not that hard. You can do it!

Well, let's do. Can I resist a you can do attitude!. Absolutely no!.

 

[eddy2017]

Thanks, let me have a try.

Given (as I was taught here to label that which has been freely given to me.
The radius of the circular pancakes increases at a rate of 1 cm per minute.
When the radius is 7 cm,
How fast is C changing?
c=2π r
c=2(3.14)(7)
Is it good so far? ( here is the radius).

 

[Romsek]

Given (as I was taught here to label that which has been freely given to me.
The radius of the circular pancakes increases at a rate of 1 cm per minute.
When the radius is 7 cm,
How fast is C changing?
c=2π r
c=2(3.14)(7)
Is it good so far? ( here is the radius).

Not really. Let's start at the beginning.

[MATH]c = 2\pi r[/MATH]
now differentiate both sides with respect to time

[MATH]\dfrac{dc}{dt} = 2\pi \dfrac{dr}{dt}[/MATH]
Are you with me so far?

Let's identify some things.

[MATH]\dfrac{dc}{dt}[/MATH] is the rate at which the circumference is changing, in this case growing.

This is what you are asked to find.

[MATH]\dfrac{dr}{dt}[/MATH] is the rate at which the radius is growing. You are given this info.

It's all plug and chug from here.

Does the current radius have an effect on the rate that the circumference grows at?

 

[eddy2017]

Not really. Let's start at the beginning.

[MATH]c = 2\pi r[/MATH]
now differentiate both sides with respect to time

[MATH]\dfrac{dc}{dt} = 2\pi \dfrac{dr}{dt}[/MATH]
Are you with me so far?

Let's identify some things.

[MATH]\dfrac{dc}{dt}[/MATH] is the rate at which the circumference is changing, in this case growing.

This is what you are asked to find.

[MATH]\dfrac{dr}{dt}[/MATH] is the rate at which the radius is growing. You are given this info.

It's all plug and chug from here.

Does the current radius have an effect on the rate that the circumference grows at?

Thanks, let me process this.

 

[eddy2017]

Not really. Let's start at the beginning.

[MATH]c = 2\pi r[/MATH]
now differentiate both sides with respect to time

[MATH]\dfrac{dc}{dt} = 2\pi \dfrac{dr}{dt}[/MATH]
Are you with me so far?

Let's identify some things.

[MATH]\dfrac{dc}{dt}[/MATH] is the rate at which the circumference is changing, in this case growing.

This is what you are asked to find.

[MATH]\dfrac{dr}{dt}[/MATH] is the rate at which the radius is growing. You are given this info.

It's all plug and chug from here.

Does the current radius have an effect on the rate that the circumference grows at?

I think I am following you .
Just a couple of questions:
d stands for what? Differentiation, I guess. If so, what does it mean in the problem at hand.
I need to know this to be certain of what I am doing and why.

 

[Romsek]

I think I am following you .
Just a couple of questions:
d stands for what? Differentiation, I guess. If so, what does it mean in the problem at hand.
I need to know this to be certain of what I am doing and why.

Can I ask what you're doing? Is this self study? Some sort of Zoom class or something? You don't even seem familiar with the basic notation.
Do you know what differentiation is? Do you have a textbook or something similar you are working through?

 

[eddy2017]

Yes, I have books. I am self- taught, though.
That is why I told you I was not familiar with the term. I began studying Math on my own, with basic knowledge that I had already had. Only basic knowledge of simple arithmetic. I saw this problem, thought it was like the ones I have been doing here in Algebra 1 and posted it

 

[eddy2017]

Yes, I have books. I am self- taught, though.
That is why I told you I was not familiar with the term. I began studying Math on my own, with basic knowledge that I had already had. Only basic knowledge of simple arithmetic. I saw this problem, thought it was like the ones I have been doing here in Algebra 1 and posted it

 

[Romsek]

Ok, I should have noted the forum and not used any terms from calculus.

I guess the key thing to note here is that as the circumference is just a constant number, 2pi, times the radius,
the rates of growth of circumference is just this same constant number time the rate of growth of the radius.

Thus the rate of growth of the circumference is just 2pi times the rate of growth of the radius.

We're told the radius grows at 1cm/minute so the circumference grows at 2pi x 1 = 2pi cm/min

Notice that this is independent of the current radius of the pancake.