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CirclesGeometryHigh schoolabout 1:22

Find the arc length and sector area for a 120° sector of a circle with radius 4: animated lesson

A narrated, step-by-step circles video lesson with captions. Final answer: r = 4, d = 8, C = 8π ≈ 25.13274123, A = 16π ≈ 50.26548246; for 120°: arc length 8π/3 ≈ 8.37758041, sector area 16π/3 ≈ 16.75516082.

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.5 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    Find the arc length and sector area for a 120° sector of a circle with radius 4.
  2. 2. Steps, part 1
    1. d=2r=8d = 2r = 8
      Diameter
    2. C=2πr=2π⋅4=8π≈25.13274123C = 2\pi r = 2\pi \cdot 4 = 8\pi \approx 25.13274123
      Circumference
    3. A=πr2=π⋅42=16π≈50.26548246A = \pi r^2 = \pi \cdot 4^2 = 16\pi \approx 50.26548246
      Area
    4. s=θ360∘⋅2πr=13⋅2π⋅4=8π3≈8.37758041s = \frac{\theta}{360^\circ} \cdot 2\pi r = \frac{1}{3} \cdot 2\pi \cdot 4 = \frac{8\pi}{3} \approx 8.37758041
      Arc length for 120°
  3. 3. Steps, part 2
    1. Asector=θ360∘πr2=16π3≈16.75516082A_{\text{sector}} = \frac{\theta}{360^\circ} \pi r^2 = \frac{16\pi}{3} \approx 16.75516082
      Sector area for 120°
  4. 4. The answer
    r=4r = 4

    r = 4, C = 8π ≈ 25.13274123, A = 16π ≈ 50.26548246

  5. 5. Check
    • C/d = 3.141592654 = π.
    • A = C·r/2 = 50.26548246.

Transcript

The problem. Here is the problem: Find the arc length and sector area for a 120° sector of a circle with radius 4. Find the radius, diameter, circumference and area of a circle from any one of them.

Steps, part 1. Diameter. Circumference. Area. Arc length for 120°.

Steps, part 2. Sector area for 120°.

The answer. So the answer is r equals 4, d equals 8, C equals 8pi approximately 25.13274123, A equals 16pi approximately 50.26548246; for 120°: arc length 8pi/3 approximately 8.37758041, sector area 16pi/3 approximately 16.75516082. Every measurement of a circle follows from its radius. The circumference grows in proportion to the radius and the area in proportion to its square.

Check. C/d equals 3.141592654 equals pi. A equals C times r/2 equals 50.26548246.

About circles

Radius, diameter, circumference and area of a circle.

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