Express the area of a circle, A, as a function of its circumference, c.A(c) = __ as a function of another variable

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The formula for the circumference of a circle is:

`c=2pir`

And the area of a circle is:

`A=pir^2`

To express the area as a function of c, we need to replace the variable r with c.

To do so, isolate the r in the formula of the circle's...

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The formula for the circumference of a circle is:

`c=2pir`

And the area of a circle is:

`A=pir^2`

To express the area as a function of c, we need to replace the variable r with c.

To do so, isolate the r in the formula of the circle's circumference.

`c=2pir`

`r=c/(2pi)`

Then, substitute this to the formula of area of a circle.

`A=pi(c/(2pi))^2`

`A=pi*c^2/(4pi^2)`

`A=c^2/(4pi)`

Hence, the area of a circle as a function of its circumference c is `A(c)=c^2/(4pi)` .

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