# Simple circle problem involving area and circumference

OK. Let's do it using limits. Let A(t) = the area at time t, and let A(t+Δt) = area at time t + Δt. Also, let C(t) = circumference at time t, and let C(t+Δt) be the circumference at time t+Δt. Starting with your general equation for A in terms of C, write an equation for A(t+Δt) - A(t) in terms of C(t+Δt) and C(t).
Ok, I need to go now. I'll answer you when I get time. I'm very sorry :/

SteamKing
Staff Emeritus
Homework Helper
Yeah sorry about that :

$$\frac{c}{2*\pi}$$
Then, if c is the circumference of the circle, the expression above can be simplified further still.

Chestermiller
Mentor
Then, if c is the circumference of the circle, the expression above can be simplified further still.
The problem statement implies expressing dA/dt entirely in terms of the circumference and its time derivative.

Chet

Then, if c is the circumference of the circle, the expression above can be simplified further still.
How ? I don't know what there is to do next.

SteamKing
Staff Emeritus
Homework Helper
How ? I don't know what there is to do next.
What's the formula for the circumference of a circle?

What's the formula for the circumference of a circle?
c=2*$\pi$*r

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SteamKing
Staff Emeritus
Homework Helper
c=2*$\pi$*r
Sigh... and what happens when you divide C by 2π ?

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Sigh... and what happens when you divide C by 2π ?
You obtian the radius. Btw why are you desesperate lol

Chestermiller
Mentor
I was hoping you would start working this problem using the method I was leading you to in post #25. This method involves using limits (which is the main requirement for your teacher). If you do what I suggested in post #25 (which is the first step in the derivation), I can lead you through, step by step, to the final result. But I need you to start.

Chet

Chestermiller
Mentor
$$A(t)=\frac{C^2(t)}{4\pi}$$
$$A(t+Δt)=\frac{C^2(t+Δt)}{4\pi}$$
$$A(t+Δt)-A(t)=\frac{C^2(t+Δt)-C^2(t)}{4\pi}$$
Do you know how to factor the numerator of the right hand side?