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A wall clock of radius 18 cm has a chord that, together with two radii from the centre, forms an equilateral triangle. If the smaller segment is painted, what is its area as a percentage of the total area of the clock (approximately)?

1. 2%
2. 3%
3. 7%
4. 9%

Correct answer: 3%

Solution

The chord with two radii forms an equilateral triangle, so the central angle is 60°. The smaller segment area equals the area of the 60° sector minus the area of the equilateral triangle. For radius 18 cm, this comes to about 30.6 cm², which is roughly 3% of the total circle area.

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