Arc Length and Sector Area

Front

What is the central angle in a circle?

Back

The central angle is the angle formed at the center of the circle by two radii. It subtends an arc on the circle.

Front

What is the formula for calculating the area of a sector?

Back

Area of a sector = (θ/360) × πr², where θ is the central angle in degrees and r is the radius.

Front

What is the formula for calculating the length of an arc?

Back

Length of an arc = (θ/360) × 2πr, where θ is the central angle in degrees and r is the radius.

Front

What is a sector in a circle?

Back

A sector is a portion of a circle enclosed by two radii and the arc between them.

Front

What is an arc in a circle?

Back

An arc is a part of the circumference of a circle.

Front

What is a segment in a circle?

Back

A segment is the area of a circle that is bounded by a chord and the arc connecting the endpoints of the chord.

Front

If the radius of a circle is 10 cm and the central angle is 60 degrees, what is the area of the sector?

Back

Area = (60/360) × π(10)² = (1/6) × 100π ≈ 52.36 cm².

Front

If the radius of a circle is 5 m and the central angle is 90 degrees, what is the length of the arc?

Back

Length = (90/360) × 2π(5) = (1/4) × 10π ≈ 7.85 m.

Front

What is the relationship between the central angle and the arc length?

Back

The arc length is directly proportional to the central angle; as the angle increases, the arc length increases.

Front

What is the difference between a sector and a segment?

Back

A sector is defined by two radii and the arc, while a segment is defined by a chord and the arc.