If the diameter of a circle is 6 inches, what is the length of the arc subtended by an angle measuring 70 degrees?

The length of an arc in a circle can be calculated using the formula:

Arc Length = (Angle / 360) * (π * Diameter)

In this case, the diameter of the circle is 6 inches. Therefore, the radius (
) would be half of the diameter:

Radius = Diameter / 2 = 6 inches / 2 = 3 inches

Now, let’s substitute the values into the arc length formula. First, calculate the circumference of the circle:

Circumference = π * Diameter = π * 6 inches

Then, the arc length for an angle of 70 degrees will be:

Arc Length = (70 / 360) * (π * 6 inches) 

Now, calculate:

Arc Length = (70 / 360) * (6π) = (7 / 36) * (6π) = (7π / 6) inches

Using the approximation of π (approximately 3.14), we can further compute:

Arc Length ≈ (7 * 3.14) / 6 ≈ 21.98 / 6 ≈ 3.66 inches

Therefore, the length of the arc subtended by a 70-degree angle in a circle with a diameter of 6 inches is approximately 3.66 inches.