Question 10

The circumference of the circle is 14π inches.

To find the circumference of a circle when the area is given, we first use the area formula \( A = πr^2 \). Given that the area is \( 49π \), we can deduce that the radius \( r \) is 7 inches. The circumference can then be calculated using the formula \( C = 2πr \), resulting in \( C = 14π \) inches.

A) 7π inches

This option is incorrect because it represents the area of the circle instead of the circumference. The area formula gives us \( 49π \) square inches, which indicates that the radius is 7 inches, but this does not relate to the circumference directly.

B) 28π inches

This option is also incorrect. If we mistakenly used a radius of 14 inches (which is double the actual radius), we would incorrectly compute the circumference as \( C = 2π(14) = 28π \) inches. However, the actual radius is only 7 inches.

C) 14π inches

This is the correct answer. Using the radius derived from the area, we calculate the circumference as \( C = 2π(7) = 14π \) inches. This correctly applies both the area and circumference formulas for circles.

D) 3.5π inches

This option is incorrect. It suggests a circumference based on a radius of 3.5 inches, which is not supported by the area given. The correct radius of 7 inches leads to a circumference of 14π inches, not 3.5π.

Conclusion

The correct answer is 14π inches, derived from the proper calculation of the radius based on the area provided. All other options either misinterpret the relationship between area and circumference or incorrectly apply the formulas.