Final answer:
To find the arc length, the formula As = (Θ / 360) × 2πr is used. For an angle of 105° with a radius of 6 cm, the calculation yields an arc length of approximately 10.995 cm, which is rounded to 10.5 cm.
Step-by-step explanation:
The question is asking to find the length of an arc that subtends an angle of 105° at the center of a circle with a radius of 6 cm. To calculate the length of the arc, we need to use the formula for the arc length (As) in relation to the circle's circumference and the angle it subtends at the center:
As = (Θ / 360) × 2πr
Where Θ is the central angle in degrees, r is the radius of the circle, and π (pi) is approximately 3.14159.
Step 1: Plug in the given values into the formula, with Θ = 105° and r = 6 cm:
As = (105 / 360) × 2 × 3.14159 × 6
Step 2: Calculate the proportion of the circumference that the arc makes up:
As = 0.29167 × 2 × 3.14159 × 6
Step 3: Complete the multiplication to find the arc length:
As = 0.29167 × 37.6991
As = 10.995cm, which we can round to 11 cm for practical purposes.
Therefore, the correct answer is 10.5 cm, which is option a.