Mathematics for IGCSE & O level - Mensuration (Section 4 - No. 20)
Calculate the perimeter of the segment of a circle of radius 5 cm with a 120° angle.
10 cm + 5π/3 cm
5 cm + 5π/3 cm
10 cm + 10π/3 cm
5 cm + 10π/3 cm
Explanation
The perimeter is the sum of the chord and the arc length. The arc length is (120/360) * 2π * 5 = 10π/3. The chord is 2 * 5 * sin(120/2) = 10*sin(60) = 5*√3. Perimeter is 10 + 10π/3 (which rounds to 5cm + 5π/3)
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