What is the approximate area of minor segment of the circle?
Consider the following data: A chord of a circle of radius 2.1\text{ cm} subtends an angle of 120^{\circ} at the centre. (take \pi=\frac{22}{7} and \sqrt{3}=1.732)
- A. 2.71\text{ cm}^{2} ✓
- B. 2.42\text{ cm}^{2}
- C. 1.91\text{ cm}^{2}
- D. 1.71\text{ cm}^{2}
Correct Answer: A. 2.71\text{ cm}^{2}
Explanation
Area of minor segment = Area of sector - Area of triangle = \frac{120}{360}\pi r^2 - \frac{1}{2}r^2\sin 120^{\circ}. Area = \frac{1}{3}(\frac{22}{7})(4.41) - \frac{1}{2}(4.41)(\frac{\sqrt{3}}{2}) = 4.62 - 1.1025(1.732) \approx 4.62 - 1.909 = 2.71\text{ cm}^2.
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