How it works
A central angle of θ degrees cuts off θ/360 of the whole circle. So
Arc length = (θ/360) × 2πr · Sector area = (θ/360) × πr²
A 90° sector is a quarter of the circle, 60° is a sixth and 120° is a third. The major arc or sector is whatever is left after the minor one: subtract from the full circle. If the question gives you the sector and asks for the angle, set up the same fraction and solve for θ.
Arcs And Sectors practice problems with solutions
These problems come from Mathyessy's question bank. Try each one before opening the solution.
A sector has central angle 90° and radius 8. Give the sector area in terms of π — enter the number before π.
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Answer: 16π
90° is a quarter of the circle. The full area is 64π, so the sector is 64π ÷ 4 = 16π.
A sector has central angle 60° and radius 12. Give the sector area in terms of π — enter the number before π.
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Answer: 24π
60° is one sixth of the circle. The full area is 144π, so the sector is 144π ÷ 6 = 24π.
A circle has radius 12. A minor arc has central angle 60°. Give the major arc length in terms of π — enter the number before π.
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Answer: 20π
The circumference is 24π. The minor arc is one sixth of it, 4π, so the major arc is 24π − 4π = 20π.
A sector has area 30π and radius 10. Find the central angle in degrees.
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Answer: 108°
The full circle has area 100π, so the sector is 30/100 of it. The angle is 0.3 × 360° = 108°.
Keep going
Related topics
- Circle area and circumference
- Polygon interior and exterior angle
- Special right triangles: 45-45-90 and 30-60-90
- Surface area
Related practice sets in the app
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