4400 Higher November 2008 Paper 3 Q19
19
Diagram NOT accurately drawn
\(AB\) is a chord of a circle, centre \(O\).
\(ACB\) is an arc of the circle.
\(OA = OB = 6.7\) cm.
Angle \(AOB = 45^\circ\).
Calculate the area of the shaded segment.
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| \(\dfrac{45}{360} \times \pi \times 6.7^2 - \dfrac{1}{2} \times 6.7^2 \times \sin 45^\circ\) | M1 |
| M1 | |
| M1 | |
| 17.628... (or 17.619...) − 15.871... | A1 |
| 1.76 or 1.75 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: for \(\dfrac{45}{360}\) oe
M1: for \(\pi \times 6.7^2\) or value which rounds to 141 seen
M1: for completely correct method of finding the area of triangle \(OAB\)
eg \(\frac{1}{2} \times 6.7^2 \times \sin 45^\circ\) or \(6.7 \times \sin 22.5^\circ \times 6.7 \times \cos 22.5^\circ\)
A1: for either area correctly evaluated rounded or truncated to 1 dp
A1: for answer rounding to 1.76 if \(\pi\) key used (\(\pi \to\) 1.7572...)
or for answer rounding to 1.75 if \(\pi = 3.14\) used (3.14 \(\to\) 1.7483...)