Discussion
The area of a sector of a circle whose radius is 12 metres and whose angle at the centre is \( 42^{\circ} \) is?
Answer: C
A sector's area is the same fraction of the circle as its angle is of a full turn.
\[ A = \frac{\theta}{360} \times \pi r^{2} \]
\[ = \frac{42}{360} \times \frac{22}{7} \times 144 \]
\[ = \frac{7}{60} \times \frac{22}{7} \times 144 = \frac{22 \times 144}{60} \]
\[ = \frac{3168}{60} = 52.8 \text{ m}^{2} \]
The whole circle covers \( \tfrac{22}{7} \times 144 = 452.6 \) m², and \( 42^{\circ} \) is just under a twelfth of it - a quick check that the answer is the right size.
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