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: $\frac{76}{7} \mathrm{~cm}$
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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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Question : The area of the sector of a circle of radius 12 cm is $32 \pi \;\mathrm{cm}^2$. Find the length of the corresponding arc of the sector.
Option 1: $\frac{16}{3} \pi$ cm
Option 2: $\frac{13}{3} \pi$ cm
Option 3: $\frac{10}{3} \pi$ cm
Option 4: $\frac{8}{3} \pi$ cm
Question : The area of a sector of a circle is 88 sq. cm., and the angle of the sector is 45°. Find the radius of the circle. (Use $\pi=\frac{22}{7}$)
Option 1: $3 \sqrt{ 11} \mathrm{~cm}$
Option 2: $4 \sqrt{ 14} \mathrm{~cm}$
Option 3: $6 \sqrt{ 13} \mathrm{~cm}$
Option 4: $5 \sqrt{ 14} \mathrm{~cm}$
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: $8 \pi ~\mathrm{cm}^2$
Question : Find the length of the arc of the sector of a circle of diameter 7 cm with a central angle of $108^{\circ}$. [Use $\pi=\frac{22}{7}$]
Option 1: 6.6 cm
Option 2: 5.6 cm
Option 3: 13.2 cm
Option 4: 11.2 cm
Question : The area of the sector of a circle (in cm2) of radius 7 cm and central angle $60^{\circ}$ is: $\left(\right.$Take $\left.\pi=\frac{22}{7}\right)$
Option 1: $\frac{77}{2}$
Option 2: $77$
Option 3: $\frac{77}{3}$
Option 4: $\frac{77}{4}$
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