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Quiz Chapter 1: Circular Measure

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

10 questions · plays in fullscreen

Full Question List & Answer Key

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

1. In a circle with centre O and radius 8 cm, triangle OAB is formed where OA = OB = 8 cm and angle AOB = 0.9 rad. What is the area of triangle OAB? (Take sin(0.9 rad) = 0.7833)

  1. 25.07 cm²
  2. 50.13 cm²
  3. 28.80 cm²
  4. 32.00 cm²
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Answer: A

Area of triangle = 12 ab sin C = 12 (8)(8) sin(0.9 rad) = 32 × 0.7833 = 25.07 cm².

2. The area of a circle is 100π cm². Calculate the area of a sector in this circle with a central angle of 0.5 rad.

  1. 50 cm²
  2. 100 cm²
  3. 25 cm²
  4. 12.5 cm²
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Answer: C

Area of circle = π r² = 100π => r = 10 cm. Area of sector = 12 r² θ = 12 (10²) (0.5) = 25 cm².

3. Convert 0.75 rad into degrees, giving your answer to two decimal places. (Take π = 3.142)

  1. 45.00°
  2. 40.11°
  3. 42.97°
  4. 43.20°
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Answer: C

0.75 rad × (180° / 3.142) = 1353.142 = 42.97°.

4. 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.

5. A pendulum of length 45 cm swings through an angle of 0.2 rad. Find the distance traveled by the tip of the pendulum.

  1. 90 cm
  2. 9 cm
  3. 4.5 cm
  4. 18 cm
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Answer: B

s = rθ = 45 × 0.2 = 9 cm.

6. 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.

7. An arc of a circle of radius 8 cm subtends an angle of 1.25 rad at the centre. Calculate the length of the arc.

  1. 6.4 cm
  2. 12.0 cm
  3. 10.0 cm
  4. 8.25 cm
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Answer: C

s = rθ = 8 × 1.25 = 10.0 cm.

8. Find the length of the chord subtending a central angle of 1.0 rad in a circle of radius 6 cm. (Take sin(0.5 rad) = 0.4794)

  1. 6.00 cm
  2. 5.75 cm
  3. 2.88 cm
  4. 3.00 cm
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Answer: B

Chord length = 2r sin(θ/2) = 2(6) sin(0.5 rad) = 12 × 0.4794 = 5.75 cm.

9. 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.

10. 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.

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