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
The Correct Answer and Explanation is:
To find the circumference of a circle given its area, follow these steps:
- Identify the given information:
- The area of the circle is 121π in2121\pi \, \text{in}^2121πin2.
- Use the formula for the area of a circle:Area=πr2\text{Area} = \pi r^2Area=πr2where rrr is the radius of the circle.
- Set up the equation with the given area:121π=πr2121\pi = \pi r^2121π=πr2
- Solve for r2r^2r2:
- Divide both sides of the equation by π\piπ: 121=r2121 = r^2121=r2
- Take the square root of both sides to find rrr: r=121=11 inr = \sqrt{121} = 11 \, \text{in}r=121=11in
- Use the formula for the circumference of a circle:Circumference=2πr\text{Circumference} = 2\pi rCircumference=2πrwhere rrr is the radius.
- Substitute rrr into the circumference formula:Circumference=2π×11\text{Circumference} = 2\pi \times 11Circumference=2π×11 Circumference=22π in\text{Circumference} = 22\pi \, \text{in}Circumference=22πin
Thus, the circumference of the circle is 22π in22\pi \, \text{in}22πin.
Explanation:
The area of a circle is given by the formula πr2\pi r^2πr2. In this problem, the area is 121π121\pi121π, which allows us to solve for the radius by isolating r2r^2r2 and taking the square root. Once we have the radius, we use the circumference formula 2πr2\pi r2πr to find the circumference. By substituting r=11r = 11r=11 inches into the circumference formula, we get 22π22\pi22π inches.
Correct answer: B. 22 π in