Area of a Segment of a Circle
This worksheet focuses on calculating the area of a segment of a circle, including understanding the relationship between sectors, triangles, and segments.
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Area of a Segment of a Circle Worksheet
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Read each question carefully and show all your work. Use π ≈ 3.14 where necessary. Round your answers to two decimal places.
1. Define what a 'segment of a circle' is in your own words. You may draw a diagram to help.
2. A circle has a radius of 10 cm. A central angle of 90° intercepts an arc. Calculate the area of the minor segment formed by this arc.
3. The area of a segment of a circle is found by subtracting the area of the from the area of the .
4. If the central angle is 180°, the segment becomes a .
5. Which formula represents the area of a sector with radius 'r' and central angle 'θ' (in degrees)?
A = rθ
A = (θ/360) * πr²
A = πr²
A = (1/2)r²θ
6. A circular pond has a radius of 5 meters. A straight path cuts across the pond, creating a segment. If the central angle subtended by the chord of the segment is 120°, find the area of the segment of the pond covered by water.
7. A segment of a circle is always smaller than its corresponding sector.
True
False
8. A regular hexagon is inscribed in a circle with a radius of 8 cm. Find the area of one of the segments formed between a side of the hexagon and the circle.