# In these problem you are asked to find a function that models a real-life situat

In these problem you are asked to find a function that models a real-life situations. Use the principle of modeling described in this Focus to help you.
Area Find a function that models the area A of a circle in terms of its circumference C.
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Calculation:
Consider the radius of circle is r.
The circumference of the circle is,
$C=2\pi r$
Here, C is circumference of a circle.
Solve the above equation for r as,
$C=2\pi r$
$\frac{C}{2\pi }=r$
$r=\frac{C}{2\pi }$
Substitute r for x in equation (1) to obtain the model that express area of circle.
$A=\pi {\left(\frac{C}{2\pi }\right)}^{2}$
$A=\frac{\pi {C}^{2}}{4{\pi }^{2}}$
$A=\frac{{C}^{2}}{4\pi }$
Conclusion:
Thus, the function that models the area of circle in terms of circumference is $A=\frac{{C}^{2}}{4\pi }$