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: $8 \pi ~\mathrm{cm}^2$
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Correct Answer: $4 \pi ~\mathrm{cm}^2$
Solution : Central angle = 40° Radius, $r$ = 6 cm Area of the sector = $\frac{\text{central angle}}{360°}×\pi r^2$ = $\frac{40°}{360°}×\pi ×6^2$ = $\frac{36}{9}×\pi $ = $4\pi$ $\mathrm{cm}^2$ Hence, the correct answer is $4\pi~\mathrm{cm}^2$.
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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 : 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 area of a sector of a circle is 110 cm2 and the central angle of the sector is 56°, what is the circle's radius? (Take $\pi=\frac{22}{7}$)
Option 1: 35 cm
Option 2: 20 cm
Option 3: 25 cm
Option 4: 15 cm
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