Question : A sector of a circle has a central angle of 45° and an arc length of 22 cm. Find the radius of the circle. ( Use $\pi=\frac{22}{7}$)

Option 1: 32 cm

Option 2: 35 cm

Option 3: 28 cm

Option 4: 36 cm

Question : The area of the sector of a circle is 128 cm². If the length of the arc of that sector is 64 cm, then find the radius of the circle.

Option 1: 4 cm

Option 2: 8 cm

Option 3: 2 cm

Option 4: 16 cm

Question : The radius of circle A is twice that of circle B and the radius of circle B is twice that of circle C. Their area will be in the ratio:

Option 1: 16 : 4 : 1

Option 2: 4 : 2 : 1

Option 3: 1 : 2 : 4

Option 4: 1 : 4 : 16

Question : Chord PQ is the perpendicular bisector of radius OA of the circle with centre O. (A is a point on the edge of the circle). If the length of Arc $PAQ=\frac{2\pi}{3}$. What is the length of chord PQ?

Option 1: $2$

Option 2: $\sqrt{3}$

Option 3: $2\sqrt{3}$

Option 4: $1$

Question : Three equal circles of unit radius touch one another. Then the area of the circle circumscribing the three circles is:

Option 1: $6 \pi (2+ \sqrt3)^2$

Option 2: $\frac{\pi}{6} (2+ \sqrt3)^2$

Option 3: $\frac{\pi}{3} (2+ \sqrt3)^2$

Option 4: $3\pi (2+ \sqrt3)^2$