What is the difference between a sector and a segment of a circle?

Sector: the region between two radii and the arc — like a 'pizza slice'. It is bounded by two straight edges (radii) and one curved edge (arc). Area = (θ/360) × πr². Segment: the region between a chord and the arc — like a 'cut-off sliver'. It is bounded by one straight edge (chord) and one curved edge (arc). Area = Area of sector − Area of triangle (formed by the two radii and chord). The main difference: sector includes the centre of the circle; segment does not.

How do you find the area of a sector?

Area of sector = (θ/360°) × πr², where θ is the central angle in degrees and r is the radius. This formula works because the full circle (360°) has area πr², and a sector is a fraction (θ/360) of the full circle. For example, a 90° sector is a quarter circle with area πr²/4. The arc length of the sector is (θ/360°) × 2πr.

What is the perimeter of a sector?

Perimeter of a sector includes two radii (straight sides) plus the arc length. Formula: Perimeter = 2r + arc length = 2r + (θ/360°) × 2πr. For example, a sector with r = 7 cm and θ = 60°: Arc length = (60/360) × 2 × 22/7 × 7 = 22/3 cm. Perimeter = 2 × 7 + 22/3 = 14 + 7.33 = 21.33 cm.

Area of Sector and Segment

Areas Related to Circles • Class 10 Mathematics • NCERT • CBSE

Area of circle = πr². Area of sector (angle θ°) = (θ/360) × πr². Length of arc = (θ/360) × 2πr. Area of minor segment = Area of sector − Area of triangle. These formulas apply to questions involving clocks, wheels, fields, and combination shapes.

Key Formulas

Area of circle = πr²
Circumference = 2πr
Area of sector = (θ/360) × πr²
Length of arc = (θ/360) × 2πr
Area of segment = Area of sector − ½r² sin θ

Frequently Asked Questions

What is the difference between a sector and a segment of a circle?: Sector: the region between two radii and the arc — like a 'pizza slice'. It is bounded by two straight edges (radii) and one curved edge (arc). Area = (θ/360) × πr². Segment: the region between a chord and the arc — like a 'cut-off sliver'. It is bounded by one straight edge (chord) and one curved edge (arc). Area = Area of sector − Area of triangle (formed by the two radii and chord). The main difference: sector includes the centre of the circle; segment does not.
How do you find the area of a sector?: Area of sector = (θ/360°) × πr², where θ is the central angle in degrees and r is the radius. This formula works because the full circle (360°) has area πr², and a sector is a fraction (θ/360) of the full circle. For example, a 90° sector is a quarter circle with area πr²/4. The arc length of the sector is (θ/360°) × 2πr.
What is the perimeter of a sector?: Perimeter of a sector includes two radii (straight sides) plus the arc length. Formula: Perimeter = 2r + arc length = 2r + (θ/360°) × 2πr. For example, a sector with r = 7 cm and θ = 60°: Arc length = (60/360) × 2 × 22/7 × 7 = 22/3 cm. Perimeter = 2 × 7 + 22/3 = 14 + 7.33 = 21.33 cm.

Study With GyanAI

GyanAI's AI tutor can answer any question about this topic instantly. Try GyanAI free for step-by-step NCERT solutions aligned with the CBSE curriculum.