A sector is a fraction of the full circle area: A sector with angle θ covers a fraction θ/360 of the full circle area (πr²).
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Worked example — sector area
Find the area of a sector with radius 10 cm and angle 108°.
Step by step
- Substitute.
Final answer
Area = 30π ≈ 94.2 cm².
Worked example — find the angle
A sector of radius 8 cm has area 32π cm². Find its angle.
Step by step
- Substitute and solve.
- Simplify.
- Rearrange.
Final answer
Angle = 180° (a semicircle).
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Worked example — find both arc and area
A sector has radius 6 cm and angle 150°. Find: (a) the arc length, (b) the area.
Step by step
- (a) Arc length.
- (b) Sector area.
Final answer
Arc length ≈ 15.7 cm; Area ≈ 47.1 cm².
Worked example — pizza slice
A circular pizza has diameter 30 cm. It is cut into 8 equal slice. Find the area of one slice.
Step by step
- Each slice has angle θ = 360/8 = 45°. Radius = 15 cm.
- Area of one slice.
Final answer
Area of one slice ≈ 88.4 cm².