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CirclesGeometryHigh schoolabout 1:21

Find the arc length and sector area for a 45° sector of a circle with radius 8: animated lesson

A narrated, step-by-step circles video lesson with captions. Final answer: r = 8, d = 16, C = 16π ≈ 50.26548246, A = 64π ≈ 201.0619298; for 45°: arc length 2π ≈ 6.283185307, sector area 8π ≈ 25.13274123.

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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. The problem
Worked example
Find the arc length and sector area for a 45° sector of a circle with radius 8.
2. Steps, part 1
1. $d = 2r = 16$
  Diameter
2. $C = 2\pi r = 2\pi \cdot 8 = 16\pi \approx 50.26548246$
  Circumference
3. $A = \pi r^2 = \pi \cdot 8^2 = 64\pi \approx 201.0619298$
  Area
4. $s = \frac{\theta}{360^\circ} \cdot 2\pi r = \frac{1}{8} \cdot 2\pi \cdot 8 = 2\pi \approx 6.283185307$
  Arc length for 45°
3. Steps, part 2
1. $A_{\text{sector}} = \frac{\theta}{360^\circ} \pi r^2 = 8\pi \approx 25.13274123$
  Sector area for 45°
4. The answer
$r = 8$
r = 8, C = 16π ≈ 50.26548246, A = 64π ≈ 201.0619298
5. Check
- C/d = 3.141592654 = π.
- A = C·r/2 = 201.0619298.

Transcript

The problem. Here is the problem: Find the arc length and sector area for a 45° sector of a circle with radius 8. Find the radius, diameter, circumference and area of a circle from any one of them.

Steps, part 1. Diameter. Circumference. Area. Arc length for 45°.

Steps, part 2. Sector area for 45°.

The answer. So the answer is r equals 8, d equals 16, C equals 16pi approximately 50.26548246, A equals 64pi approximately 201.0619298; for 45°: arc length 2pi approximately 6.283185307, sector area 8pi approximately 25.13274123. 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 201.0619298.

About circles

Radius, diameter, circumference and area of a circle.

Find the arc length and sector area for a 45° sector of a…