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
The Correct Answer and Explanation is:
To determine the circumference of a circle when given its area, follow these steps:
Step 1: Find the Radius from the Area
The formula for the area of a circle is given by: A=πr2A = \pi r^2A=πr2 where AAA is the area and rrr is the radius.
You are given the area of the circle as 9π9\pi9π square inches. Set this equal to the formula for the area: 9π=πr29\pi = \pi r^29π=πr2
To solve for r2r^2r2, divide both sides by π\piπ: 9=r29 = r^29=r2
Next, take the square root of both sides to find rrr: r=9r = \sqrt{9}r=9 r=3 inchesr = 3 \text{ inches}r=3 inches
Step 2: Calculate the Circumference
The formula for the circumference CCC of a circle is: C=2πrC = 2 \pi rC=2πr
Substitute the value of rrr (which is 3 inches) into the formula: C=2π×3C = 2 \pi \times 3C=2π×3 C=6π inchesC = 6 \pi \text{ inches}C=6π inches
Conclusion
The circumference of the circle is 6π6\pi6π inches.
Explanation
To recap, the area of a circle is dependent on the square of the radius, and the circumference is directly proportional to the radius. By rearranging the area formula, we determined the radius of the circle and then used this radius to compute the circumference. The steps show how each measurement (area and circumference) relates through the radius, providing a clear path from one to the other. This illustrates not only how to find the circumference given the area but also the interconnectedness of these fundamental geometric properties. The correct answer is:
B. 6 π in