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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Correct Answer: 8 cm
Solution : Given: The area of a sector of a circle of radius 28 cm is 112 cm2. The area of a sector of a circle of radius $r=\pi\times r^2 \times \frac{\theta}{360^\circ}$ ⇒ $\frac{22}{7} \times 28^2 \times \frac{\theta}{360^\circ} = 112$ ⇒ $\theta = \frac{360^\circ}{22}$ So, the length of the arc of the sector $=2 \pi r × \frac{\theta}{360^\circ}$ $=2 \times \frac{22}{7} \times 28 \times \frac{360^\circ}{22 × 360^\circ}$ $= 8$ cm Hence, the correct answer is 8 cm.
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Question : What is the area of the sector of a circle of radius 8 cm and formed by an arc of length 12 cm?
Option 1: 45 cm2
Option 2: 47 cm2
Option 3: 48 cm2
Option 4: 84 cm2
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 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 : 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
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
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