A circle has an area of 121π in2. Which of the following is the circumference of the circle in terms of pi (π)?
A.
11 π in
B.
22 π in
C.
44 π in
D.
5.5 π in
To find the circumference of the circle given its area, follow these steps:
- Start with the formula for the area of a circle:Area=πr2\text{Area} = \pi r^2Area=πr2Here, the area is given as 121π121\pi121π.
- Set up the equation:πr2=121π\pi r^2 = 121\piπr2=121π
- Solve for r2r^2r2:r2=121r^2 = 121r2=121
- Take the square root of both sides to find rrr:r=121=11r = \sqrt{121} = 11r=121=11
- Use the radius to find the circumference of the circle using the formula:Circumference=2πr\text{Circumference} = 2\pi rCircumference=2πrSubstitute r=11r = 11r=11:Circumference=2π×11=22π\text{Circumference} = 2\pi \times 11 = 22\piCircumference=2π×11=22π
Therefore, the circumference of the circle is B. 22 π in.