Find the length of arc $ABC$.

Find the area of the shaded region.

correct substitution     (A1)

eg$\;\;\;l = 1.3 \times 3$

$l$  = $3.9$ (cm)     A1     N2

[2 marks]

METHOD 1

valid approach     (M1)

eg$\;\;\;$finding reflex angle, $2\pi  - {\rm{C\hat OA}}$

correct angle     (A1)

eg$\;\;\;2\pi  - 1.3,{\text{ }}4.98318$

correct substitution     (A1)

eg$\;\;\;\frac{1}{2}(2\pi  - 1.3){3^2}$

$22.4243$

${\text{area}} = 9\pi  - 5.85{\text{ (exact), }}22.4{\text{ }} {\text{ }}({\text{c}}{{\text{m}}^2})$     A1     N3

METHOD 2

correct area of small sector     (A1)

eg$\;\;\;\frac{1}{2}(1.3){3^2},{\text{ }}5.85$

valid approach     (M1)

eg$\;\;\;$circle − small sector, $\pi {r^2} - \frac{1}{2}\theta {r^2}$

correct substitution     (A1)

eg$\;\;\;\pi ({3^2}) - \frac{1}{2}(1.3){3^2}$

$22.4243$

${\text{area}} = 9\pi  - 5.85{\text{ }}({\text{exact}}),{\text{ }}22.4{\text{ }}{\text{ }}({\text{c}}{{\text{m}}^2})$     A1     N3

[4 marks]

Total [6 marks]