Flash Cards: Areas Related to Circles

A sector is the portion of a circular region enclosed by two radii and the arc connecting them.

A segment is the area enclosed between a chord and the arc of the circle.

The minor segment is the smaller area between a chord and the arc, while the major segment is the larger area.

Area of a sector = (πrq) / 360, where 'r' is the radius and 'q' is the angle in degrees.

Length of an arc = (2πrq) / 360, where 'r' is the radius and 'q' is the angle in degrees.

Area of a segment = Area of the sector - Area of the triangle formed by the radii and chord.

Confusing the area of a sector with the area of a segment is a common mistake.

To convert degrees to radians, multiply by (π/180).

Use the formula for the area of a quarter circle: A = (πr²)/4 where r = circumference/(2π).

Use the formula: Area = (1/2) * base * height, with the base being the chord length.

Total Area = πr², where 'r' is the radius.

Area of major sector = Total area of circle - Area of minor sector.

Unless stated, use π = 3.14 or π = 22/7 depending on the problem.

Area = Sector area = (θ/360) * πr², where θ is the angle swept by the hand.

A quadrant is a sector that represents 90 degrees of the circle.

Use the formula: Chord Length = 2r * sin(θ/2) where r is the radius and θ is the angle.

π is essential for calculations involving circles, representing the ratio of circumference to diameter.