A circular sector has a central angle of 120 degrees and a radius of 9 cm. What is the perimeter of the sector?
Answer and explanation
Correct answer: A. 6pi + 18 cm
- Step 1: The perimeter of a circular sector consists of the arc length L plus the two bounding radii: Perimeter = L + 2r.
- Step 2: Convert angle to radians: theta = 120 * (pi / 180) = 2pi / 3 radians.
- Step 3: Arc length L = r theta = 9 (2pi / 3) = 6pi cm.
- Step 4: Add the two radii: 2r = 2 * 9 = 18 cm.
- Step 5: Total perimeter = 6pi + 18 cm.
Answer
6pi + 18 cm.
Why not the others: '6pi cm' is only the curved arc length without the two straight radius edges; '18pi + 18 cm' uses the full circle circumference instead of 1/3; '27pi cm' calculates the sector area (1/2 r^2 theta = 1/2 81 2pi/3 = 27pi cm^2).
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