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

`A=8.2 cm^2` or
`A=(81)/(\pi )`

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\\(18)/(2\pi ) =(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 ((9)/(\pi )) ^(2) \\A=(81)/(\pi )`