0580/22 May/Jun 2021, Question 19: Arc Length
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 6 marks
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The question, in short
Use an equilateral triangle of side 12.4 cm with a circle sector centred at A to find a perimeter, then use a shaded major sector of area 74.5 cm² with a 41° minor sector to find the radius.
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Part (a) · 3 marks
Find the perimeter of the shape formed by the equilateral triangle and the major sector bounded by chord BC and the major arc.
- 1Angle of the major sector = 360 − 60 = 300°
- 2Major arc = 300/360 × 2 × π × 12.4 = 64.92…
- 3Perimeter = 64.92… + 12.4
- 4= 77.32… ≈ 77.3 cm
Answer77.3 or 77.32 to 77.33…
Part (b) · 3 marks
Given the major sector area 74.5 cm² and minor sector angle 41°, calculate the circle's radius.
- 1Angle of the major sector = 360 − 41 = 319°
- 274.5 = 319/360 × π × r²
- 3r² = 74.5 × 360 ÷ (319π) = 26.76…
- 4r = 5.172… ≈ 5.17 cm
Answer5.17 or 5.172 to 5.173…
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Also searched as: 0580/22/M/J/21 · 0580_s21_qp_22 · 0580 s21 22 · question 19.
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