Question : Find the area of the sector of a circle with a radius of 4 cm containing an angle of 30°.
Option 1: 7.186 cm2
Option 2: 6.186 cm2
Option 3: 4.186 cm2
Option 4: 5.186 cm2
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Correct Answer: 4.186 cm2
Solution : Radius = 4 cm Angle = 30° Area = $\frac{ \theta}{360°}×\pi r^2$ ⇒ Area = $\frac{30}{360}×3.14 \times 4^2$ ⇒ Area = $3.14 \times \frac{4}{3}$ ⇒ Area = $4.186$ cm2 The area of the sector of a circle with a radius of 4 cm and an angle of 30° is 4.186 cm2. Hence, the correct answer is 4.186 cm2.
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Question : Find the area of the sector of a circle with a radius of 5 cm and an angle of 60° (rounded off to one decimal).
Option 1: 12.8 cm2
Option 2: 14.1 cm2
Option 3: 13.1 cm2
Option 4: 15.1 cm2
Question : The area of a sector of a circle is 308 cm2, with the central angle measuring 45°. The radius of the circle is:
Option 1: 14 cm
Option 2: 21 cm
Option 3: 7 cm
Option 4: 28 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
Question : A sector of a circle of radius 10 cm is formed at a 60° angle at the centre. What will be its area $($take $\pi=3.14)?$
Option 1: 52.33 cm2
Option 2: 75.28 cm2
Option 3: 60.67 cm2
Option 4: 55.00 cm2
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
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