A circular clock has a radius of 12 cm. A chord along with two radii forms an equilateral triangle at the center. The smaller segment formed by the chord is painted. What percentage of the clock's total area is this segment? (Use π = 3.14, √3 = 1.732)
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 2.88%.
Total area of clock = πr2 = 3.14 × 122 = 452.16 cm2
For an equilateral triangle at the center, the central angle = 60°
Area of sector = (60/360) × Area of circle = (1/6) × 452.16 = 75.36 cm2
Area of equilateral triangle = (√3/4)a2 = (1.732/4) × 122 = 0.433 × 144 = 62.352 cm2
Area of segment = 75.36 − 62.352 = 13.008 cm2
Percentage of painted segment = (13.008/452.16) × 100 ≈ 2.88%