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It should be noted that the length of an arc between two consecutive spokes is 2.3562.
From the information given, the following can be noted:
Radius = 3 inches
Angle of arc = 360°/8 = 45° = π/4
The length of the arc will be:
= π/4 × 3
= 3π/4
= 2.3562
The area of the sector will be:
= πr² × [3π/(4 × 2π)]
= π(3)² × 3π/8π
= 27π/8 inches²
In conclusion, the area of the sector is 27π/8 inches².
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