Question

Find the radius of the circle in which a central angle of

60∘ intercepts an arc of length 37.4 cm.

Answer 1

To find the radius of the circle in which a central angle of 60∘ intercepts an arc of length 37.4 cm, use the formula for the circumference of a circle.

Step-by-step explanation:

To find the radius of the circle in which a central angle of 60∘ intercepts an arc of length 37.4 cm, we can use the formula for the circumference of a circle.

Since the central angle is 60 degrees, it represents one-sixth of a full revolution. Therefore, the angle A in radians is 60∘ / 180∘ * π = π/3.

Now, we can use the formula for the circumference of a circle, C = 2πr, where C is the arc length and r is the radius. Rearranging the formula, we have r = C / (2π).

Substituting the values into the formula, we get r = 37.4 cm / (2π) ≈ 5.944 cm.