Question : Find the perimeter of a major sector of a circle of radius 12 metres, whose minor sector subtends an angle of 75° at the centre.
Option 1: $(24 + 5π)$ metres
Option 2: $(24 + 19π)$ metres
Option 3: $(24 – 5π)$ metres
Option 4: $(24 – 19π)$ metres
Correct Answer: $(24 + 19π)$ metres
Solution : Here, we have a radius of the circle = 12 m and a minor sector angle subtends an angle = 75º Angle subtended by major arc = 360º – 75º = 285º Perimeter of major arc = $2 \times \pi \times r \times \frac{\theta}{360º} + 2r$ $= 2 \times \pi \times 12 \times \frac{285º}{360º} + 2 \times 12$ $= (19\pi + 24$) metres Hence, the correct answer is ($24 + 19\pi$) meters.
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