1. ## Circle Math

If the circumference of a circle increases by 20%, how much is the area increased by?

2. ## Re: Circle Math

Originally Posted by harpazo
If the circumference of a circle increases by 20%, how much is the area increased by?
For the circumference to increase what must change?
How does that change effect the area?

3. ## Re: Circle Math

Are you not aware by now that the rule at Math Help Boards
is to show your work, and where you're stuck??????

Start by TRYING a case; as example:
circumference = c = 20
calculate area A.

circumference = 1.2c = 24
calculate area A + ?

4. ## Re: Circle Math

Originally Posted by harpazo
If the circumference of a circle increases by 20%, how much is the area increased by?
Area changes by the square of line length (in any shape, not just circles). In this case your factor for line length is 1.2 (new circumference is 120% of the old). So the new area is $1.2^2$ times that of the old.

5. ## Re: Circle Math

Originally Posted by Archie
Area changes by the square of line length (in any shape, not just circles). In this case your factor for line length is 1.2 (new circumference is 120% of the old). So the new area is $1.2^2$ times that of the old.
What exactly are you saying here?
Can you set up the equation for me?

6. ## Re: Circle Math

Originally Posted by harpazo
What exactly are you saying here?
Can you set up the equation for me?
Ummmmm...... He just did.

If a length change is made (in this case a circle which is 1-D) then a corresponding change to an area is indicated.

So if we have a circle with circumference C and we increase it by 20% then the new circumference is now 1.2C. So the corresponding area (originally A) would increase by a factor of $\displaystyle 1.2^2$, ie. the new area is $\displaystyle 1.2^2A$.

-Dan

7. ## Re: Circle Math

Originally Posted by harpazo
What exactly are you saying here?
Can you set up the equation for me?
Originally Posted by harpazo
If the circumference of a circle increases by 20%, how much is the area increased by?
To harpazo: You did not answer my reply: "For the circumference to increase what must change?"
Well, the circumference is $\pi D=\pi\cdot 2r$ where $D$ is diameter & $r$ is radius.
The old area is $\pi r^2$ and the new increased area is $\pi(1.2r)^2$.
Remember what that I told you before the percent of change is $\dfrac{New-Old}{Old}$. SEE HERE.

8. ## Re: Circle Math

Thank you everyone.