O-LevelAdditional MathematicsCircular measure4037/22 · May/June 2013 · Q67 Marks
The shaded region in the diagram is a segment of a circle with centre O and radius r cm. Angle AOB = π/3 radians.
- (i)Show that the perimeter of the segment is r(3 + π/3) cm.[2]
- (ii)Given that the perimeter of the segment is 26cm, find the value of r and the area of the segment.[5]
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Mark scheme
Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.
- [B1] (i) arc AB = r(π/3)
- [B1] (i) chord AB = r with justification and summation and completion to given answer
- [B1] (ii) r = 12.7
- [M3] (ii) (1/2) x their r² x (π/3) - (1/2) x their r² x sin(π/3) o.e.
- [A1] (ii) awrt 14.6
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