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Quiz Chapter 1: Circular Measure

10 questions · Form 5 Additional Mathematics Bab 1: Circular Measure

Question 1 of 10Score: 0

A sector has an area of 50 cm² and a radius of 10 cm. Find the arc length of the sector.

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. A sector has an area of 50 cm² and a radius of 10 cm. Find the arc length of the sector.

  1. 10 cm
  2. 20 cm
  3. 5 cm
  4. 15 cm
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Answer: A

A = 12 r s => 50 = 12 (10) s => 50 = 5s => s = 10 cm.

2. The minor arc AB of a circle with centre O and radius 7 cm has a length of 11 cm. Find the major angle AOB in radians. (Take π = 3.142)

  1. 4.71 rad
  2. 1.57 rad
  3. 3.14 rad
  4. 2.00 rad
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Answer: A

Minor angle θ = sr = 117 = 1.571 rad. Major angle = 2π - 1.571 = 2(3.142) - 1.571 = 6.284 - 1.571 = 4.713 rad.

3. A sector of a circle has a radius of 6 cm and an area of 27 cm². Find the central angle subtended in radians.

  1. 1.5 rad
  2. 2.25 rad
  3. 0.75 rad
  4. 1.2 rad
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Answer: A

Area A = 12 r² θ => 27 = 12 (6²) θ => 27 = 18θ => θ = 2718 = 1.5 rad.

4. An arc length of 15 cm subtends an angle of 1.5 rad at the centre of a circle. What is the radius of the circle?

  1. 10 cm
  2. 22.5 cm
  3. 12 cm
  4. 15 cm
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Answer: A

s = rθ => 15 = r(1.5) => r = 151.5 = 10 cm.

5. Find the perimeter of a sector with a radius of 10 cm and a central angle of 0.8 rad.

  1. 8 cm
  2. 28 cm
  3. 18 cm
  4. 20.8 cm
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Answer: B

Arc length s = rθ = 10 × 0.8 = 8 cm. Perimeter = s + 2r = 8 + 2(10) = 28 cm.

6. If the arc length of a circle is equal to twice its radius, what is the central angle in radians?

  1. 1.0 rad
  2. π rad
  3. 0.5 rad
  4. 2.0 rad
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Answer: D

s = rθ => 2r = rθ => θ = 2.0 rad.

7. Find the area of the minor segment subtended by an angle of π3 rad in a circle of radius 6 cm.

  1. 18.85 cm²
  2. 3.26 cm²
  3. 15.59 cm²
  4. 6.52 cm²
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Answer: B

Sector area = 12 (6²) (π3) = 6π ≈ 18.85 cm². Triangle area = 12 (6²) sin(60°) = 18 × (√32) ≈ 15.59 cm². Segment area = 18.85 - 15.59 = 3.26 cm².

8. The perimeter of a sector of a circle of radius r cm is 25 cm. If the angle at the centre is 1.5 rad, find the value of r.

  1. 8.33 cm
  2. 10.00 cm
  3. 16.67 cm
  4. 7.14 cm
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Answer: D

Perimeter = rθ + 2r = r(θ + 2). 25 = r(1.5 + 2) => 25 = 3.5r => r = 253.5 = 7.14 cm.

9. Convert 5π6 radians to degrees.

  1. 120°
  2. 150°
  3. 210°
  4. 135°
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Answer: B

(5π6) × (180°/π) = 5 × 30° = 150°.

10. A wheel rotates through 15 complete revolutions. What is the total angle rotated in radians?

  1. 15π rad
  2. 30π rad
  3. 60π rad
  4. 45π rad
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Answer: B

1 revolution = 2π rad. 15 revolutions = 15 × 2π = 30π rad.

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