35. A circle has an area of 49π square inches. What is the circumference of the circle in terms ofπ?
Answer: B
The circumference of the circle is 14π inches.
To find the circumference of a circle when the area is given, we first use the formula for the area, which is A = πr². Given that the area is 49π, we can solve for the radius r, and then use that to find the circumference using the formula C = 2πr.
A) 7π in
This option suggests a circumference of 7π inches. However, if we calculate the radius from the area, we find that the radius is 7 inches (since r² = 49), leading to a circumference of 14π inches. Therefore, this option is incorrect.
B) 14π in
This option is correct. By determining the radius from the area (49π = πr²), we find r = 7 inches. The circumference is then calculated as C = 2πr = 2π(7) = 14π inches, confirming that this option is accurate.
C) 28π in
This option indicates a circumference of 28π inches. If we apply the formula for circumference, C = 2πr, with the radius of 7 inches, we find C = 14π inches, not 28π inches. Thus, this option is incorrect.
D) 3.5π in
This option implies a circumference of 3.5π inches. However, using the radius derived from the area, the correct circumference is 14π inches. Therefore, this option is also incorrect.
Conclusion
The correct answer is 14π inches, derived from calculating the radius of the circle from its area. All other options either miscalculate the radius or apply the circumference formula incorrectly, affirming that only option B accurately represents the circumference in terms of π.