Paper 22 Q11IGCSE 0580 May/June 2023

Question

11 B 2.6 cm C NOT TO 3.2 cm SCALE O D A The diagram shows a shape, ABCD, formed by the sectors of two circles with the same centre O. Both sector angles are 140°, OC=3.2cm and CB=2.6cm. The area of the shape is krcm^{2}. Find the value of k.

Diagram: # Diagram Description **Diagram type:** Two concentric circular sectors with shared centre O, forming a composite shape ABCD **Key measurements/labels:** - OC = 3.2 cm - CB = 2.6 cm - Both sector angles = 140° - Points labeled: O (centre), A, B, C, D **Key relationships:** - "NOT TO SCALE" notice present - ABCD is formed by two sectors of circles with the same centre O - The sectors are concentric (share centre O) - OA = OB (radii of outer sector) - OC = OD = 3.2 cm (radii of inner sector) - CB = 2.6 cm (radial width between the two sectors)

This question tests your ability to find the area of a shape formed by two concentric sectors. You need to understand that the shape ABCD is the difference between a larger sector and a smaller sector.

Step-by-Step Solution

Key Takeaway

When finding the area of a shape between two concentric sectors, subtract the inner sector area from the outer sector area.

Common Mistakes

Using CB = 2.6 cm as a radius instead of recognising it's the width between the circles
Forgetting to convert the angle fraction 140/360 to its simplest form 7/18, leading to calculation errors

Exam Tip

Always identify what each measurement represents in the diagram - some are radii, others might be widths or chord lengths.

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