Question : A circular arc whose radius is 4 cm makes an angle of 45º at the centre. Find the perimeter of the sector formed. (Take $\pi=\frac{22}{7}$)
Option 1: $\frac{78}{7} \mathrm{~cm}$
Option 2: $\frac{72}{7} \mathrm{~cm}$
Option 3: $\frac{74}{7} \mathrm{~cm}$
Option 4: $\frac{76}{7} \mathrm{~cm}$
Correct Answer: $\frac{78}{7} \mathrm{~cm}$
Solution :
A circular arc whose radius is 4 cm makes an angle of 45° at the centre.
Here, radius($r$) = 4 cm and central angle($\theta$) = 45°.
We know,
The perimeter of the sector in circle = $2\pi r×(\frac{\theta}{360°})$ + 2 × $r$
= $2×\frac{22}{7}×4×\frac{45°}{360°}$ + 8
= $\frac{78}{7} \mathrm{~cm}$
Hence, the correct answer is $\frac{78}{7} \mathrm{~cm}$.
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