Foundation January 2019 Paper 1 Q17
17 The diagram shows an isosceles triangle \(ABC\) and a semicircle with centre \(O\) and diameter 12 cm.
The point \(B\) lies on the semicircle.
Diagram NOT accurately drawn
The line \(OB\) is the line of symmetry of the diagram.
\(AC\) is 1 cm from the diameter of the semicircle and \(AC = 8\) cm.
Work out the area of the shaded region.
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
| \(\dfrac{\pi \times 6^2}{2}\) oe or 56.5(4866....) or \(18\pi\) | M2 |
| \(\dfrac{1}{2} \times 8 \times (6 - 1)\) or 20 oe | M1 |
| 36.5 | A1 |
| (4) | |
| (4 marks) |
Notes
M2: If not M2 then award M1 for \(\pi \times 6^2\) oe (= 113(.09)) or \(36\pi\)
M1: for the area of the triangle
A1: for 36.5 – 36.6