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Question (11)

QN0036981

11. The area of a sector of angle θ and radius r is:

(A) θ/180 × πr²
(B) θ/360 × πr²
(C) θ/360 × 2πr
(D) 360/θ × πr²

Correct Answer: B

Explanation:

Area of sector = θ/360 × πr².

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Question (12)

QN0036982

12. A sector of radius 14 cm and angle 135° has area:

(A) 154 cm²
(B) 231 cm²
(C) 308 cm²
(D) 462 cm²

Correct Answer: B

Explanation:

Area = 135/360 × 22/7 × 14² = 231 cm².

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Question (13)

QN0036983

13. The radius of a circle is 21 cm. A sector has angle 60°. Its area is:

(A) 154 cm²
(B) 231 cm²
(C) 462 cm²
(D) 693 cm²

Correct Answer: B

Explanation:

Area = 60/360 × 22/7 × 21² = 231 cm².

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Question (14)

QN0036984

14. A circle has radius 28 cm. The area of a sector is 308 cm². Taking π = 22/7, the angle of the sector is:

(A) 30°
(B) 45°
(C) 60°
(D) 90°

Correct Answer: B

Explanation:

Area of circle = 2464 cm². Since 308/2464 = 1/8, the angle = 360°/8 = 45°.

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Question (15)

QN0036985

15. The length of an arc of a sector of radius r and angle θ is:

(A) θ/360 × πr²
(B) θ/180 × πr
(C) θ/360 × 2πr
(D) 360/θ × 2πr

Correct Answer: C

Explanation:

Arc length = θ/360 × 2πr.

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Question (16)

QN0036986

16. A circle has radius 14 cm. Find the length of the arc corresponding to a sector of 45°. Take π = 22/7.

(A) 7 cm
(B) 11 cm
(C) 14 cm
(D) 22 cm

Correct Answer: B

Explanation:

Arc length = 45/360 × 2 × 22/7 × 14 = 11 cm.

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Question (17)

QN0036987

17. A sector has radius 21 cm and arc length 22 cm. Taking π = 22/7, its central angle is:

(A) 30°
(B) 45°
(C) 60°
(D) 90°

Correct Answer: C

Explanation:

22 = θ/360 × 2 × 22/7 × 21. Therefore θ = 60°.

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Question (18)

QN0036988

18. If the radius of a circle is doubled while the central angle remains unchanged, the area of the corresponding sector becomes:

(A) Half
(B) Double
(C) Four times
(D) Eight times

Correct Answer: C

Explanation:

Sector area is proportional to r². Doubling the radius makes the area four times.

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Question (19)

QN0036989

19. If the radius of a circle is doubled and the sector angle is halved, the area of the sector becomes:

(A) Half
(B) Double
(C) Four times
(D) Unchanged

Correct Answer: B

Explanation:

New area/old area = 1/2 × 2² = 2. Hence the area doubles.

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Question (20)

QN0036990

20. A sector of radius 7 cm subtends 180° at the centre. Its area is:

(A) 38.5 cm²
(B) 77 cm²
(C) 154 cm²
(D) 308 cm²

Correct Answer: B

Explanation:

A 180° sector is a semicircle. Area = 1/2 × 22/7 × 7² = 77 cm².

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Question (11)

11. The area of a sector of angle θ and radius r is:

Explanation:

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Question (12)

12. A sector of radius 14 cm and angle 135° has area:

Explanation:

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Question (13)

13. The radius of a circle is 21 cm. A sector has angle 60°. Its area is:

Explanation:

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Question (14)

14. A circle has radius 28 cm. The area of a sector is 308 cm². Taking π = 22/7, the angle of the sector is:

Explanation:

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Question (15)

15. The length of an arc of a sector of radius r and angle θ is:

Explanation:

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Question (16)

16. A circle has radius 14 cm. Find the length of the arc corresponding to a sector of 45°. Take π = 22/7.

Explanation:

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Question (17)

17. A sector has radius 21 cm and arc length 22 cm. Taking π = 22/7, its central angle is:

Explanation:

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Question (18)

18. If the radius of a circle is doubled while the central angle remains unchanged, the area of the corresponding sector becomes:

Explanation:

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Question (19)

19. If the radius of a circle is doubled and the sector angle is halved, the area of the sector becomes:

Explanation:

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Question (20)

20. A sector of radius 7 cm subtends 180° at the centre. Its area is:

Explanation:

Link:

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