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
The Correct answer and Explanation is:
To solve this problem, we need to determine the circumference of the circle given its area. The key to solving this lies in understanding the relationship between the area, radius, and circumference of a circle.
Step 1: Use the formula for the area of a circle.
The area AAA of a circle is given by the formula:A=πr2A = \pi r^2A=πr2
where rrr is the radius of the circle.
Step 2: Plug in the given area.
We know the area of the circle is 49π49\pi49π square inches:49π=πr249\pi = \pi r^249π=πr2
Step 3: Solve for the radius.
To find the radius rrr, divide both sides by π\piπ:r2=49r^2 = 49r2=49
Taking the square root of both sides gives:r=49=7 inchesr = \sqrt{49} = 7 \text{ inches}r=49=7 inches
Step 4: Use the formula for the circumference of a circle.
The circumference CCC of a circle is given by the formula:C=2πrC = 2\pi rC=2πr
Substitute the radius r=7r = 7r=7 inches into the formula:C=2π(7)=14π inchesC = 2\pi(7) = 14\pi \text{ inches}C=2π(7)=14π inches
Conclusion:
The correct answer is A. 14π in.
Explanation:
The area of the circle was provided as 49π49\pi49π square inches. Using the area formula A=πr2A = \pi r^2A=πr2, we found the radius rrr to be 7 inches. With this radius, we applied the circumference formula C=2πrC = 2\pi rC=2πr and calculated the circumference to be 14π14\pi14π inches. The key steps involved recognizing how to extract the radius from the area and then applying it to the circumference formula. Understanding these fundamental formulas allows us to transition between area, radius, and circumference, highlighting their interconnectedness.