The diagram shows a metal plate made by removing a segment from a circle with centre O and radius 8 cm. The line AB is a chord of the circle and angle AOB = 2.4 radians. Find [Figure 6.1]

Mark scheme

Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.

1. [M1] Uses cosine rule (AB² = 8² + 8² - 2(8)(8)cos(2.4)) or 2r sin(θ/2) (AB = 2 * 8 * sin(2.4/2)); Any complete valid method.
2. [A1] → 14.9 cm; co.
3. [M1] Perimeter = Length AB + Major arc length. Major arc length = r * (2π - 2.4); Uses s = rθ with 2.4, or π – 2.4, or 2π – 2.4.
4. [B1] Correct angle for major arc (2π - 2.4); Anywhere in parts (ii) or (iii).
5. [A1] → 46.0 cm; Adds 31.06 to (i) for major arc length.
6. [M1] Area = Area of major sector + Area of triangle AOB; Uses ½r²θ. Uses any valid method.
7. [M1] Area = ½ * 8² * (2π - 2.4) + ½ * 8² * sin(2.4); co for both terms.
8. [A1] → 146 cm²; co.