A circle has an area of 9 (pi) in2. Which of the following is the circumference of the circle in terms of pi ((pi))?
A.
12 π in
B.
6 π in
C.
9 π in
D.
3 π in
To find the circumference of a circle given its area, follow these steps:
- Find the radius:
- The area of a circle is given by the formula A=πr2A = \pi r^2A=πr2.
- Given the area A=9πA = 9\piA=9π, set up the equation: 9π=πr29\pi = \pi r^29π=πr2
- Divide both sides by π\piπ: 9=r29 = r^29=r2
- Take the square root of both sides: r=9=3r = \sqrt{9} = 3r=9=3
- Find the circumference:
- The circumference of a circle is given by the formula C=2πrC = 2\pi rC=2πr.
- Substitute r=3r = 3r=3 into the formula: C=2π×3=6πC = 2\pi \times 3 = 6\piC=2π×3=6π
So, the circumference of the circle is 6π6\pi6π inches.
B. 6 π in