Question

The circumference of a circle is 278.71m. What is the approximate area of the circle? Use 3.14 for pi. Explain how the area of a circle changes when the circumference of a circle changes ( round the final answer to the nearest whole number as needed , round all the intermediate values to the nearest thousandth as needed )

Answer 1

The circumference of a circle can be found through the formula:

`C=2\cdot\pi\cdot r`

clear the equation for the radius

`r=(C)/(2\pi)`

find the radius of the circumference

`\begin{gathered} r=(278.71)/(2\pi) \\ r\approx44.358 \end{gathered}`

find the area of the circle using the formula

`\begin{gathered} A=\pi\cdot r^2 \\ A=\pi\cdot(44.358)^2 \\ A\approx6181 \end{gathered}`