Question : The radius of a circle is 21 cm. What will be the length (in cm) of an arc of the circle that subtends a 22.5° angle at the centre? [Use $\pi=\frac{22}{7}$]
Option 1: 8.25
Option 2: 7.25
Option 3: 8.50
Option 4: 7.50
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Correct Answer: 8.25
Solution : We know that arc length = $\frac{2\pi r \times \theta}{360}$ So, given $\theta = 22.5°$ Radius of circle = $21$ cm $\therefore$ Length of the arc = $\frac{2 \times 22 \times 21 \times 22.5}{360 \times 7}$ = 8.25 cm Hence, the correct answer is 8.25.
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Question : In a circle with centre O, arc CD subtends an angle of 60° at the centre of the circle whose radius is 21 cm. Calculate the length of the arc CD.
Option 1: 20 cm
Option 2: 18 cm
Option 3: 24 cm
Option 4: 22 cm
Question : In a circle, an arc subtends an angle of 84° at the centre. If the length of the arc is 22 cm, then the radius of the circle (in cm) is equal to: Take $\pi=\frac{22}{7}$
Option 1: 19
Option 2: 15
Option 3: 17
Option 4: 13
Question : The arc length of a sector of a circle that subtends a $22.5^{\circ}$ angle at the centre is given as $16.5$ cm. What will be the radius (in cm) of the circle? [Use $\pi=\frac{22}{7}$]
Option 1: 35
Option 2: 49
Option 3: 42
Option 4: 48
Question : In a circle of radius 14 cm, an arc subtends an angle of 90° at the centre. The length of are (in cm) is equal to: (Take $\pi=\frac{22}{7}$)
Option 1: 22
Option 2: 18
Option 3: 20
Option 4: 24
Question : The area of a sector of a circle that subtends a 22.5° angle at the centre is given as 346.5 cm². What will be the radius (in cm) of the circle? [Use $\pi=\frac{22}{7}$]
Option 2: 45
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