Arc Length and Sector Area

Front

What is the green area called?

Back

Sector

Front

What is the ϴ called?

Back

Central angle

Front

Find the measure of arc AB if the total circumference is 340 degrees and the arc measures 68 degrees.

Back

68 degrees

Front

What is the length L called in a circle?

Back

Arc

Front

What is the formula for the area of a sector?

Back

Area = (θ/360) * π * r², where θ is the central angle in degrees and r is the radius.

Front

What is the formula for arc length?

Back

Arc Length = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius.

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 = 17.45 cm² (approximately).

Front

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

Back

Arc Length = (90/360) * 2π * 5 = 7.85 cm (approximately).

Front

What is the difference between a sector and a segment in a circle?

Back

A sector is the area enclosed by two radii and the arc, while a segment is the area between a chord and the arc.

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.