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Question (21)

QN0036991

21. A circular disc of radius 14 cm is divided into 8 equal sectors. The area of each sector is:

(A) 49 cm²
(B) 77 cm²
(C) 98 cm²
(D) 154 cm²

Correct Answer: B

Explanation:

Area of circle = 22/7 × 14² = 616 cm². Area of each sector = 616/8 = 77 cm².

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Question (22)

QN0036992

22. A sector of radius 14 cm has an angle of 120°. Its arc length is:

(A) 22 cm
(B) 88/3 cm
(C) 28 cm
(D) 44 cm

Correct Answer: B

Explanation:

Arc length = 120/360 × 2 × 22/7 × 14 = 88/3 cm.

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Question (23)

QN0036993

23. A chord divides a circle into a minor segment and a major segment. If the minor segment has area 80 cm² and the whole circle has area 500 cm², the major segment has area:

(A) 400 cm²
(B) 420 cm²
(C) 480 cm²
(D) 580 cm²

Correct Answer: B

Explanation:

Major segment = area of circle - area of minor segment = 500 - 80 = 420 cm².

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Question (24)

QN0036994

24. The area of a minor segment is obtained by subtracting the area of which figure from the corresponding sector?

(A) Circle
(B) Rectangle
(C) Triangle
(D) Semicircle

Correct Answer: C

Explanation:

Area of segment = Area of sector - Area of corresponding triangle.

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Question (25)

QN0036995

25. A sector has radius 14 cm and central angle 90°. The corresponding triangle formed by the two radii and chord is a right isosceles triangle. Its area is:

(A) 49 cm²
(B) 98 cm²
(C) 154 cm²
(D) 196 cm²

Correct Answer: B

Explanation:

The two perpendicular sides are 14 cm each. Area = 1/2 × 14 × 14 = 98 cm².

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Question (26)

QN0036996

26. A circle of radius 14 cm has a chord subtending 90° at the centre. Using π = 22/7, the area of the corresponding minor segment is:

(A) 56 cm²
(B) 98 cm²
(C) 154 cm²
(D) 252 cm²

Correct Answer: A

Explanation:

Sector area = 154 cm² and triangle area = 98 cm². Segment area = 154 - 98 = 56 cm².

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Question (27)

QN0036997

27. A chord of a circle of radius 10 cm subtends 60° at the centre. Using π = 3.14 and √3 = 1.73, the area of the corresponding minor segment is approximately:

(A) is the closest.
(B) 17.33 cm²
(C) 25.67 cm²
(D) 31.40 cm²

Correct Answer: A

Explanation:

Sector area = 52.33 cm². Triangle area = 1/2 × 10 × 10 × √3/2 = 43.25 cm². Segment area ≈ 52.33 - 43.25 = 9.08 cm², approximately 9 cm². Using √3 = 1.73 gives about 9.08 cm²; option (a) is the closest.

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Question (28)

QN0036998

28. A sector of radius 21 cm and angle 120° has area 462 cm². If the corresponding triangle has area 300 cm², the area of the minor segment is:

(A) 162 cm²
(B) 300 cm²
(C) 462 cm²
(D) 762 cm²

Correct Answer: A

Explanation:

Segment area = sector area - triangle area = 462 - 300 = 162 cm².

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Question (29)

QN0036999

29. A circle has radius 21 cm. An arc subtends 60° at the centre. The length of the arc is:

(A) 11 cm
(B) 22 cm
(C) 44 cm
(D) 66 cm

Correct Answer: B

Explanation:

Arc length = 60/360 × 2 × 22/7 × 21 = 22 cm.

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Question (30)

QN0037000

30. A circle of radius 14 cm has a sector of 135°. What is the area of the corresponding major sector?

(A) 231 cm²
(B) 385 cm²
(C) 462 cm²
(D) 616 cm²

Correct Answer: B

Explanation:

Minor sector area = 135/360 × 616 = 231 cm². Major sector = 616 - 231 = 385 cm².

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Question (21)

21. A circular disc of radius 14 cm is divided into 8 equal sectors. The area of each sector is:

Explanation:

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Question (22)

22. A sector of radius 14 cm has an angle of 120°. Its arc length is:

Explanation:

Link:

Question (23)

23. A chord divides a circle into a minor segment and a major segment. If the minor segment has area 80 cm² and the whole circle has area 500 cm², the major segment has area:

Explanation:

Link:

Question (24)

24. The area of a minor segment is obtained by subtracting the area of which figure from the corresponding sector?

Explanation:

Link:

Question (25)

25. A sector has radius 14 cm and central angle 90°. The corresponding triangle formed by the two radii and chord is a right isosceles triangle. Its area is:

Explanation:

Link:

Question (26)

26. A circle of radius 14 cm has a chord subtending 90° at the centre. Using π = 22/7, the area of the corresponding minor segment is:

Explanation:

Link:

Question (27)

27. A chord of a circle of radius 10 cm subtends 60° at the centre. Using π = 3.14 and √3 = 1.73, the area of the corresponding minor segment is approximately:

Explanation:

Link:

Question (28)

28. A sector of radius 21 cm and angle 120° has area 462 cm². If the corresponding triangle has area 300 cm², the area of the minor segment is:

Explanation:

Link:

Question (29)

29. A circle has radius 21 cm. An arc subtends 60° at the centre. The length of the arc is:

Explanation:

Link:

Question (30)

30. A circle of radius 14 cm has a sector of 135°. What is the area of the corresponding major sector?

Explanation:

Link:

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