Question

Geometry Question

12. A circle has a radius of 12 feet. What is the length of an arc of that circle that is captured by a central angle that measures 128 degrees? Round your answer to the nearest hundredth.

26.81 feet
20.73 feet
13.42 feet
14.27 feet

Answer 1

The length of an arc of a circle is given by the formula L = (θ/360) × 2πr, where θ is the central angle in degrees, r is the radius of the circle, and π is approximately equal to 3.14.

Substituting the given values, we get:

L = (128/360) × 2π(12)
L = (0.356) × 2π(12)
L = (0.356) × 24π
L = 8.52π

Rounding to the nearest hundredth, we get:

L ≈ 26.81 feet

Therefore, the answer is (A) 26.81 feet.