Answer: The length of an arc of a circle is given by the formula:
L = rθ
where L is the length of the arc, r is the radius of the circle, and θ is the central angle in radians.
To find the length of the bottom arc, we have:
L1 = r1θ1
where r1 = 5 inches and θ1 = 135° = (135/180)π radians.
L1 = 5(135/180)π = 16.88 inches (rounded to two decimal places)
To find the length of the top arc, we have:
L2 = r2θ2
where r2 = 23 inches and θ2 = 135° = (135/180)π radians.
L2 = 23(135/180)π = 29.07 inches (rounded to two decimal places)
The difference in length between the top arc and the bottom arc is:
L2 - L1 = 29.07 - 16.88 ≈ 12
Therefore, to the nearest inch, the top arc is 12 inches longer than the bottom arc.
Explanation: