Question : The area of a sector of a circle is 66 cm² and the angle of the sector is 60°. Find the radius of the circle.

Option 1: $5 \sqrt{15} \mathrm{~cm}$

Option 2: $6 \sqrt{14} \mathrm{~cm}$

Option 3: $7 \sqrt{19} \mathrm{~cm} $

Option 4: $3 \sqrt{14} \mathrm{~cm} $

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

Question : The volume of a cone with a height equal to the radius and slant height of 5 cm is:

Option 1: $\frac{125 \pi}{12 \sqrt{3}} \mathrm{~cm}^3$

Option 2: $\frac{125 \pi}{6 \sqrt{3}} \mathrm{~cm}^3$

Option 3: $\frac{125 \pi}{12 \sqrt{2}} \mathrm{~cm}^3$

Option 4: $\frac{125 \pi}{6 \sqrt{2}} \mathrm{~cm}^3$