Mathematical Methods · Unit 1 · Trigonometric functions · Circular measure and radian measure
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A circular sector has radius 6 m and subtends an angle of 2.4 radians at the centre. (a) Calculate the arc length of the sector. [1 mark] (b) Calculate the area of the sector. [2 marks] (c) A second sector from the same circle has an area of 27 m². Determine the angle subtended by the second sector at the centre. [1 mark]
Calculate the perimeter (cm) of a sector with radius 8 cm and central angle \(\frac{5\pi}{9}\) radians.
A circular garden bed has a radius of $ 8 \text{ m} $. A sector of the garden is designed with a central angle of $ 72° $. (a) Calculate the arc length of this sector. Give your answer to the nearest whole metre. [1 mark] (b) Calculate the area of the sector. Give your answer to the nearest square metre. [2 marks]
A water tank has a circular cross-section with radius 2.5 m. A sector of the tank is cordoned off for maintenance work. The sector has a central angle of π/3 radians. Calculate: (a) the arc length of the sector boundary (1 mark) (b) the area of the sector (2 marks)