Question

Find the area of the circle with a circumference of 30π. write your solution in terms of π

Answer 1

we know that

the circumference of a circle is giving by

`C=2\pi r`

we have

C=30pi

substitute

`\begin{gathered} 30\pi=2\pi r \\ \text{simplify} \\ r=(30)/(2) \\ r=15\text{ units} \end{gathered}`

Find the area of the circle

`A=\pi r^2`

substitute the value of r

`\begin{gathered} A=\pi(15^2) \\ A=225\pi\text{ unit\textasciicircum{}2} \end{gathered}`

the area is 225π square units