A wire in the shape of a circular arc with a central angle of $120^{\circ}$ has its ends mounted on the top edge of a rectangular board. This board is hung on a nail in the wall as shown in Figure 1, with the midpoint of the wire aligned with the nail, so that the long sides of the board are parallel to the ground. Then this wire is removed, bent into a semicircle shape, and mounted on the board again. The board is hung on the same nail as shown in Figure 2, with the midpoint of the wire again aligned with the nail, so that the long sides of the board are again parallel to the ground. As a result, the height of the board from the ground decreases by 8 units compared to the initial position. What is the length of the wire? A) $24\pi$ B) $28\pi$ C) $32\pi$ D) $36\pi$ E) $40\pi$
A wire in the shape of a circular arc with a central angle of $120^{\circ}$ has its ends mounted on the top edge of a rectangular board. This board is hung on a nail in the wall as shown in Figure 1, with the midpoint of the wire aligned with the nail, so that the long sides of the board are parallel to the ground.
Then this wire is removed, bent into a semicircle shape, and mounted on the board again. The board is hung on the same nail as shown in Figure 2, with the midpoint of the wire again aligned with the nail, so that the long sides of the board are again parallel to the ground. As a result, the height of the board from the ground decreases by 8 units compared to the initial position.
What is the length of the wire?
A) $24\pi$
B) $28\pi$
C) $32\pi$
D) $36\pi$
E) $40\pi$