Area of a Segment of a Circle Worksheet
Calculate the area of segments of circles using given radii and central angles, applying advanced geometric formulas.
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Area of a Segment of a Circle
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Read each question carefully and calculate the area of the circular segment. Show all your work. Use π ≈ 3.14159. Round your final answers to two decimal places.
1. A circle has a radius of 10 cm. A segment is formed by a chord that subtends a central angle of 90°. Calculate the area of this segment.
2. The area of a circular sector with radius 'r' and central angle 'θ' (in radians) is given by the formula: Area = .
3. The area of a triangle formed by two radii and a chord in a circle is given by the formula: Area = (where 'r' is the radius and 'θ' is the central angle in radians).
4. Which of the following formulas correctly represents the area of a segment of a circle?
A = r²θ
A = (1/2)r²(θ - sinθ)
A = πr²(θ/360)
A = (1/2)r²sinθ
5. A circular garden has a radius of 15 meters. A path cuts across the garden, forming a chord that subtends a central angle of 120°. Find the area of the smaller segment of the garden.
6. If the central angle of a sector is 180°, the area of the segment is equal to the area of the semicircle.
True
False
7. A circular window has a radius of 0.5 meters. A decorative bar cuts across the window, forming a segment with a central angle of 60°. What is the area of the glass in this segment?