Answer:
16pi/9 in
Explanation:
length of arc = (angle/360) x (2πr)
where angle is the central angle of the arc in degrees, r is the radius of the circle, and π is the mathematical constant pi (approximately equal to 3.14159).
In this case, the radius is given as 8 inches and the central angle is 40 degrees. Substituting these values into the formula, we get:
length of arc = (40/360) x (2π x 8)
length of arc = (1/9) x (16π)
length of arc = 16π/9
So the length of the arc is 16π/9 inches. Rounded to the nearest hundredth, this is approximately 5.60 inches. Therefore, the answer is 16 pi 1/9 inches, when expressed in mixed number form.