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

Full Question List & Answer Key

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1. 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.

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. Calculate the area of a segment of a circle with radius 5 cm subtended by an angle of 1.2 rad at the centre. (Take π = 3.142)

  1. 3.35 cm²
  2. 15.00 cm²
  3. 11.65 cm²
  4. 6.70 cm²
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Answer: A

Area of sector = 12 (5²) (1.2) = 15 cm². Area of triangle = 12 (5²) sin(1.2 rad) = 12.5 × 0.9320 = 11.65 cm². Area of segment = 15 - 11.65 = 3.35 cm².

4. 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.

5. 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.

6. 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.

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. 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°.

9. 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.

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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