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Question (41)

QN0037011

41. A circular brooch of diameter 35 mm is divided into 10 equal sectors. Taking π = 22/7, the area of each sector is:

(A) 48.125 mm²
(B) 96.25 mm²
(C) 192.5 mm²
(D) 385 mm²

Correct Answer: B

Explanation:

Radius = 17.5 mm. Total area = 22/7 × 17.5² = 962.5 mm². Each sector = 962.5/10 = 96.25 mm².

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Question (42)

QN0037012

42. A circular table has radius 28 cm and is divided into 6 equal sectors. The area of each sector is approximately:

(A) 205.3 cm²
(B) 410.7 cm²
(C) 616 cm²
(D) 1232 cm²

Correct Answer: B

Explanation:

Total area = 22/7 × 28² = 2464 cm². Each sector = 2464/6 ≈ 410.7 cm².

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Question (43)

QN0037013

43. If the area of a sector is 154 cm² and the radius is 14 cm, its central angle is:

(A) 45°
(B) 60°
(C) 90°
(D) 120°

Correct Answer: C

Explanation:

Area of complete circle = 616 cm². Since 154/616 = 1/4, the angle = 360°/4 = 90°.

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Question (44)

QN0037014

44. A sector has radius 21 cm and angle 120°. If its area is 462 cm², what is the area of the corresponding major sector?

(A) 924 cm²
(B) 1155 cm²
(C) 1386 cm²
(D) 1848 cm²

Correct Answer: A

Explanation:

Complete circle area = 22/7 × 21² = 1386 cm². Major sector = 1386 - 462 = 924 cm².

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Question (45)

QN0037015

45. The radius of a circular track is 35 m. The length of an arc corresponding to 72° is:

(A) 22 m
(B) 44 m
(C) 55 m
(D) 70 m

Correct Answer: B

Explanation:

Arc length = 72/360 × 2 × 22/7 × 35 = 44 m.

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Question (46)

QN0037016

46. A sector has radius 14 cm. If its arc length is 22 cm, its central angle is:

(A) 45°
(B) 90°
(C) 120°
(D) 180°

Correct Answer: D

Explanation:

22 = θ/360 × 2 × 22/7 × 14. Solving gives θ = 180°.

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Question (47)

QN0037017

47. A circular region has radius 10 cm. A sector of angle 144° is removed from it. The angle of the remaining sector is:

(A) 144°
(B) 180°
(C) 216°
(D) 288°

Correct Answer: C

Explanation:

Remaining angle = 360° - 144° = 216°.

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Question (48)

QN0037018

48. A sector has radius 12 cm and angle 150°. If π = 3.14, its area is:

(A) 157 cm²
(B) 188.4 cm²
(C) 226.1 cm²
(D) 314 cm²

Correct Answer: B

Explanation:

Area = 150/360 × 3.14 × 12² = 188.4 cm².

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Question (49)

QN0037019

49. The area of a sector is directly proportional to its central angle when the radius is fixed. If a 40° sector has area 50 cm², the area of a 120° sector of the same circle is:

(A) 100 cm²
(B) 120 cm²
(C) 150 cm²
(D) 200 cm²

Correct Answer: C

Explanation:

120° is three times 40°, so the area is 3 × 50 = 150 cm².

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Question (50)

QN0037020

50. A circular region has area 1540 cm². A sector of angle 72° is formed in it. The area of this sector is:

(A) 154 cm²
(B) 308 cm²
(C) 462 cm²
(D) 616 cm²

Correct Answer: B

Explanation:

Sector fraction = 72/360 = 1/5. Area = 1540/5 = 308 cm².

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Question (41)

41. A circular brooch of diameter 35 mm is divided into 10 equal sectors. Taking π = 22/7, the area of each sector is:

Explanation:

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Question (42)

42. A circular table has radius 28 cm and is divided into 6 equal sectors. The area of each sector is approximately:

Explanation:

Link:

Question (43)

43. If the area of a sector is 154 cm² and the radius is 14 cm, its central angle is:

Explanation:

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Question (44)

44. A sector has radius 21 cm and angle 120°. If its area is 462 cm², what is the area of the corresponding major sector?

Explanation:

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Question (45)

45. The radius of a circular track is 35 m. The length of an arc corresponding to 72° is:

Explanation:

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Question (46)

46. A sector has radius 14 cm. If its arc length is 22 cm, its central angle is:

Explanation:

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Question (47)

47. A circular region has radius 10 cm. A sector of angle 144° is removed from it. The angle of the remaining sector is:

Explanation:

Link:

Question (48)

48. A sector has radius 12 cm and angle 150°. If π = 3.14, its area is:

Explanation:

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Question (49)

49. The area of a sector is directly proportional to its central angle when the radius is fixed. If a 40° sector has area 50 cm², the area of a 120° sector of the same circle is:

Explanation:

Link:

Question (50)

50. A circular region has area 1540 cm². A sector of angle 72° is formed in it. The area of this sector is:

Explanation:

Link:

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