Question

The area of a circle is 100π ft². What is the circumference, in feet? express your answer in terms of \piπ

Answer 1

20π ft

Explanation:

To find the circumference of the circle given its area, first find its radius.

`\textcolor{steelblue}{\boxed{\text{Area of circle =}\pi {r}^(2) }}`

Substitute given area into the formula:

100π= πr²

Divide both sides by π:

100= r²

Square root both sides:

`r = √(100)`

r= 10 ft

`\textcolor{steelblue}{\boxed{\text{Circumference of circle = }2\pi {r}}}`

Since we have found the value of the radius, we can substitute r= 10 into the formula above to find the circumference.

Circumference of circle

= 2(π)(10)

= 20π ft