Question : The radius of a circle with centre at O is 6 cm and the central angle of a sector is 40°. Find the area of the sector.
Option 1: $6 \pi ~\mathrm{cm}^2$
Option 2: $5 \pi ~\mathrm{cm}^2$
Option 3: $4 \pi ~\mathrm{cm}^2$
Option 4: $8 \pi ~\mathrm{cm}^2$
Correct Answer: $4 \pi ~\mathrm{cm}^2$
Solution :
Central angle = 40°
Radius, $r$ = 6 cm
Area of the sector = $\frac{\text{central angle}}{360°}×\pi r^2$
= $\frac{40°}{360°}×\pi ×6^2$
= $\frac{36}{9}×\pi $
= $4\pi$ $\mathrm{cm}^2$
Hence, the correct answer is $4\pi~\mathrm{cm}^2$.
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