10 Questions
Match the following formulas with the correct concept in geometry:
Area of Sector = θ × π/360 × r^2 = Sector area Area of Segment = (θ × π/360 - sin(θ)/2) × r^2 = Segment area Central Angle = The angle formed by two radii of a circle Arc Length = θ × π/180 × r = Arc length
Match the following descriptions with the correct concept in geometry:
A part of a circle enclosed by two radii and an arc = Sector A part of a circle cut by a chord that intersects at two points = Segment The angle that a sector of a circle subtends at the center = Central angle The perimeter of a segment formed by a chord and the arc = Segment perimeter
Match the following components with their roles in calculating area:
θ = Central angle r = Radius of the circle sin(θ) = Sine function in segment area formula π = Constant in area formulas
Match the following terms with their corresponding formulas:
Area of Sector = θ × π/360 × r^2 Area of Segment = (θ × π/360 - sin(θ)/2) × r^2 Arc Length = θ × π/180 × r Segment Perimeter = Length of the chord + Arc length
Match the following statements with the correct component in geometry:
A line segment that intersects the circle at two points = Chord The angle formed by two radii of a circle = Central angle A circular region partitioned by two radii and an arc = Sector A circular region partitioned by a chord that intersects the circle at two points = Segment
The perimeter of a segment is the sum of the lengths of the two radii and the ______ that forms the segment.
arc
The area of a sector is the area of the circle between two radii and the ______ that forms the sector.
arc
A central angle is an angle with its vertex at the center of a circle and its sides extending to the endpoints of an ______.
arc
The perimeter of a segment is given by: Perimeter of Segment = (theta/360) * 2pi r + ______
2r
The area of a sector is given by: Area of Sector = (theta/360) * pi r^2. Here, theta is the measure of the central angle in degrees, r is the radius of the circle, and pi is a mathematical constant (approximately 3.14). This formula is derived by dividing the area of the circle by the number of sectors, which is 360, and then multiplying it by the central angle in ______.
degrees
Study Notes
Sectors and Segments of a Circle
A circle is a simple, smooth, and curved shape with all points equidistant from the center. Our focus in this article is on sectors and segments of a circle, which are essential concepts in geometry.
Sectors and Segments
A sector is a part of a circle enclosed by two radii and an arc. A sector is created when a circular region is partitioned by two radii that start at the center and end at the circumference.
A segment is a part of a circle cut by a chord, which is a line segment that intersects the circle at two points. A segment is created when a circular region is partitioned by a chord that intersects the circle at two points.
Sector Area
The area of a sector can be found using the formula:
Area of Sector = θ × π360 × r2 (when θ is in degrees)
Where:
- θ is the central angle of the sector in degrees
- r is the radius of the circle
Segment Area
The area of a segment can be found by subtracting the area of a triangle formed by the chord and the two radii from the area of the sector:
Area of Segment = (θ × π360 - sin(θ)2) × r2 (when θ is in radians)
Central Angle
The central angle is the angle formed by two radii of a circle. It is the angle that a sector of a circle subtends at the center of the circle.
Arc Length
The arc length of a sector or segment can be found using the formula:
Arc Length = θ × r (when θ is in radians)
Segment Perimeter
The perimeter of a segment is the sum of the lengths of the chord and the arc. It can be calculated using the formula:
Perimeter = chord length + arc length
In conclusion, sectors and segments are essential concepts in geometry. Understanding their properties, such as area, arc length, and perimeter, allows us to analyze and manipulate circular regions in various ways.
Learn about the essential concepts of sectors and segments of a circle in geometry. Explore how to calculate the area, arc length, and perimeter of sectors and segments, as well as understand the properties of central angles.
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