2025 CCHY PRELIMS P2 Q4

In the diagram, \(O\) is the centre of a circular picture \(ACBQ\) of radius \(20\text{ m}\).
\(APB\) is an arc of a circle centre \(C\) and radii \(AC\) and \(BC\).
\(COQ\) is a diameter of the circular picture \(ACBQ\).
\(COQ\) bisects \(AB\) at \(M\).

If angle \(ACB=1.4\) radians,

1. show that \(AC\) is approximately \(30.594\text{ m}\),

   [3]

2. calculate the perimeter of the shaded region,

   [3]

3. calculate the total cost of painting the sector \(OAQB\) if the painting cost is \(\$0.50\) per square metre.

   [3]