Practice Maths

Arc Length and Sector Area — Solutions

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  1. Fraction of a circle

    1. 90°:
    2. 180°:
    3. 60°:
    4. 270°:
    5. 120°:
    6. 45°:
    7. 30°:
    8. 240°:

  2. Arc length

    1. r=5, θ=90°:
    2. r=10, θ=180°:
    3. r=6, θ=60°:
    4. r=8, θ=45°:
    5. r=12, θ=120°:
    6. r=4, θ=270°:
    7. r=3, θ=30°:
    8. r=15, θ=144°:

  3. Sector area

    1. r=4, θ=90°:
    2. r=7, θ=180°:
    3. r=6, θ=60°:
    4. r=10, θ=45°:
    5. r=5, θ=270°:
    6. r=9, θ=120°:
    7. r=2, θ=30°:
    8. r=8, θ=150°:

  4. Perimeter of sector

    1. r=6, θ=90°:
    2. r=10, θ=60°:
    3. r=5, θ=120°:
    4. r=8, θ=270°:
    5. r=3, θ=45°:
    6. r=12, θ=30°:

  5. Find unknown angle or radius

    1. r=6, arc=6π → θ:
    2. θ=120°, area=12π → r:
    3. r=10, area=25π → θ:
    4. Semicircle perimeter=36.28:

  6. Real-world arc and sector problems

    1. Clock minute hand r=12 cm, 20 min:
    2. Pie r=15 cm, 8 slices:
      1. Angle per slice:
      2. Arc length:
      3. Area of one slice:
    3. Sector garden r=5, θ=150°, $12/m²:
    4. Sector B same area as Sector A:

  7. Arc length and sector area from diagrams Understanding

  8. Sector table Understanding

  9. Spot the error Understanding

  10. Extended response Problem Solving