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CirclesGeometryHigh schoolabout 1:20

Find the arc length and sector area for a 90° sector of a circle with radius 10: animated lesson

A narrated, step-by-step circles video lesson with captions. Final answer: r = 10, d = 20, C = 20π ≈ 62.83185307, A = 100π ≈ 314.1592654; for 90°: arc length 5π ≈ 15.70796327, sector area 25π ≈ 78.53981634.

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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 90° sector of a circle with radius 10.
2. Steps, part 1
1. $d = 2r = 20$
  Diameter
2. $C = 2\pi r = 2\pi \cdot 10 = 20\pi \approx 62.83185307$
  Circumference
3. $A = \pi r^2 = \pi \cdot 10^2 = 100\pi \approx 314.1592654$
  Area
4. $s = \frac{\theta}{360^\circ} \cdot 2\pi r = \frac{1}{4} \cdot 2\pi \cdot 10 = 5\pi \approx 15.70796327$
  Arc length for 90°
3. Steps, part 2
1. $A_{\text{sector}} = \frac{\theta}{360^\circ} \pi r^2 = 25\pi \approx 78.53981634$
  Sector area for 90°
4. The answer
$r = 10$
r = 10, C = 20π ≈ 62.83185307, A = 100π ≈ 314.1592654
5. Check
- C/d = 3.141592654 = π.
- A = C·r/2 = 314.1592654.

Transcript

The problem. Here is the problem: Find the arc length and sector area for a 90° sector of a circle with radius 10. Find the radius, diameter, circumference and area of a circle from any one of them.

Steps, part 1. Diameter. Circumference. Area. Arc length for 90°.

Steps, part 2. Sector area for 90°.

The answer. So the answer is r equals 10, d equals 20, C equals 20pi approximately 62.83185307, A equals 100pi approximately 314.1592654; for 90°: arc length 5pi approximately 15.70796327, sector area 25pi approximately 78.53981634. 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 314.1592654.

About circles

Radius, diameter, circumference and area of a circle.

Find the arc length and sector area for a 90° sector of a…