To find the length of the arc subtended by an angle in a circle, we can use the formula:
L = (θ / 360) × C
where L is the arc length, θ is the angle in degrees, and C is the circumference of the circle.
First, we need to calculate the circumference (C) of the circle. The formula for the circumference is:
C = π × d
where d is the diameter. Here, the diameter is 6 inches, so:
C = π × 6 ≈ 18.85 inches.
Next, we can substitute the values into the arc length formula. The angle θ is 70 degrees:
L = (70 / 360) × 18.85 ≈ 36.45 inches.
Therefore, the length of the arc subtended by a 70-degree angle in a circle with a diameter of 6 inches is approximately 3.65 inches.