Question

The circumference of a particular circle is 18 cm. In square centimeters, what is the area of the circle? Express your answer as a common fraction in terms of pi.

Answer 1

Answer:

$A=8.2 cm^2$ or $A=\frac{81}{\pi }$

Step-by-step explanation:

Since the the formula for the circumference of a circle is $C=2\pi r$ and C is 18, we can substitute and solve for r. After we solve for r, we substitute it into the area formula.

$18=2\pi r\\\frac{18}{2\pi } =\frac{2\pi r}{2\pi }\\2.866=r$

The formula for the area is $A=\pi r^{2} \\A=\pi 2.866^{2} \\A=8.2 cm^2$

As a fraction, we would not simplify to a decimal and the solution would be:

$A=\pi r^{2} \\A=\pi (\frac{9}{\pi }) ^{2} \\A=\frac{81}{\pi }$