O-LevelMathematicsMensuration4024/11 · May/June 2013 · Q194 Marks

The diagram shows the metal cover for a circular drain. Water drains out through the shaded sections. O is the centre of circles with radii 1 cm, 2 cm, 3 cm, 4 cm and 5 cm. The cover has rotational symmetry of order 6 and BÔC = 40°. [Diagram showing concentric circles with sectors shaded in an alternating pattern]

(a)Calculate the area of the shaded section ABCD, giving your answer in terms of π.[2]
(b)(i)The total area of the metal (unshaded) sections of the cover is 55/3 π cm². Calculate the total area of the shaded sections, giving your answer in terms of π.[1]
(b)(ii)Calculate the fraction of the total area of the cover that is metal (unshaded). Give your answer in its simplest form.[1]

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Topic: Mensuration, O-Level Mathematics (syllabus 4024). Structured question, 4 marks.
Source: O-Level Mathematics, May/June 2013 Paper 1 Variant 1, question 19.

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