A circle has an area of 49π in2. Which of the following is the circumference of the circle in terms of pi (π)?
A.
14 π in
B.
28 π in
C.
7 π in
D.
3.5 π in
To find the circumference of the circle given its area, follow these steps:
- Find the radius:The formula for the area of a circle is:A=πr2A = \pi r^2A=πr2Given A=49πA = 49\piA=49π, we can set up the equation:49π=πr249\pi = \pi r^249π=πr2To solve for r2r^2r2, divide both sides by π\piπ:49=r249 = r^249=r2Taking the square root of both sides gives:r=49=7r = \sqrt{49} = 7r=49=7
- Find the circumference:The formula for the circumference of a circle is:C=2πrC = 2\pi rC=2πrSubstituting r=7r = 7r=7:C=2π×7=14πC = 2\pi \times 7 = 14\piC=2π×7=14π
So, the circumference of the circle is:
A. 14 π in