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 : The area of a sector of a circle of radius 28 cm is 112 cm². Find the length of the corresponding arc of the sector.

Option 1: 4 cm

Option 2: 8 cm

Option 3: 6 cm

Option 4: 5 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 : Two circles touch each other externally. The radius of the first circle with centre O is 12 cm. Radius of the second circle with centre A is 8 cm. Find the length of their common tangent BC.

Option 1: $6 \sqrt{6} \mathrm{~cm}$

Option 2: $8 \sqrt{3} \mathrm{~cm}$

Option 3: $8 \sqrt{2} \mathrm{~cm}$

Option 4: $8 \sqrt{6} \mathrm{~cm}$

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: $\frac{76}{7} \mathrm{~cm}$