Question : A horse is grazing in a field. It is tied to a pole with a rope of length 6 m. The horse moves from point A to point B making an arch with an angle of 70°. Find the area of the sector grazed by the horse.
Option 1: 22 m$^2$
Option 2: 21 m$^2$
Option 3: 23 m$^2$
Option 4: 20 m$^2$
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Correct Answer: 22 m$^2$
Solution :
Given,
Radius, $r$ = 6 m
Central angle, $\theta$ = 70°
So, the required area = $\pi\times 6^2 \times \frac{70°}{360°}$
$=\frac{22}{7}\times 36\times \frac{70°}{360°}$
$= 22\text{ m}^2$
Hence, the correct answer is 22 m$^2$.
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