27 exam-style questions on Radians; sector area and arc length in radians — topic 3.7 of Geometry and Trigonometry in the IB Mathematics: Applications and Interpretation syllabus — with answers and explanations. Samples below; the full set is free with an account.
Convert 135° to radians, giving your answer as an exact multiple of π.
Answer: 3π/4
135° × π/180 = 135π/180 = 3π/4 radians.
A sector of a circle of radius 6 cm has a central angle of 2 radians. Calculate the area of the sector, in cm².
Answer: 36
Sector area = 1/2 r²θ = 1/2 × 6² × 2 = 1/2 × 36 × 2 = 36 cm².
A sector has arc length 15 cm and radius 5 cm. Determine the central angle, in radians.
Answer: 3
From arc length = rθ, θ = arc length / r = 15 / 5 = 3 radians.
Convert π/9 radians to degrees.
Answer: 20°
π/9 × 180/π = 180/9 = 20°.
A sector of radius 9 cm has central angle π/3 radians. Calculate the area of the sector, to 3 s.f., in cm².
Answer: 42.4
Area = 1/2 r²θ = 1/2 × 81 × π/3 = 81π/6 = 13.5π ≈ 42.4 cm².
A pendulum of length 0.75 m swings through an angle of 0.4 radians. Calculate the distance travelled by the tip of the pendulum, in m.
Answer: 0.3
The tip traces an arc: length = rθ = 0.75 × 0.4 = 0.3 m.
That was 6 of 27 Radians; sector area and arc length in radians questions.
Practise all 27 freeStateAO1 · 1–2 marks
One word or one short sentence. No explanation, no working: the mark is for the fact itself.
ExplainAO3 · 1–3 marks
Give reasons or causes: say what happens AND why, linking each step with 'because' or 'so that'.
27 Radians; sector area and arc length in radians questions — free with an account. Spaced repetition, streaks and full exam simulations included.
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