A circle has an area of 49π square inches. What is the circumference of the circle in terms ofπ?

Rationale

The circumference of the circle is 14π inches.

The area of a circle is given by the formula A = πr², where r is the radius of the circle. Given that the area is 49π square inches, we can set up the equation 49π = πr² to solve for r. The radius is therefore 7 inches. The circumference of a circle is given by the formula C = 2πr, so substituting 7 inches for r gives a circumference of 14π inches.

A (7π in) YOUR ANSWER

This would be the correct answer if we were asked for the diameter of the circle, not the circumference. The diameter is twice the radius, and since the radius is 7 inches, the diameter would indeed be 7π inches.

B (14π in) CORRECT

This is the correct answer, as explained above. The circumference of a circle is given by the formula C = 2πr, and substituting 7 inches for r (the radius we calculated from the given area) gives a circumference of 14π inches.

C (28π in) YOUR ANSWER

This answer is incorrect because it is twice the correct circumference. A circumference of 28π inches would correspond to a circle with a radius of 14 inches, not 7 inches.

D (3.5π in) YOUR ANSWER

This answer is incorrect because it is half the correct circumference. A circumference of 3.5π inches would correspond to a circle with a radius of 1.75 inches, not 7 inches.

Conclusion

The circumference of a circle can be found using the formula C = 2πr, where r is the radius of the circle. Given an area of 49π square inches, we first find the radius to be 7 inches. Substituting this into the circumference formula gives us a circumference of 14π inches. The other options either overestimate or underestimate the correct circumference by a factor of 2.

A circle has an area of 49π square inches. What is the circumference of the circle in terms ofπ?

The circumference of the circle is 14π inches.

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