Finding Arc Length and Area of Sector

Front

What is the formula for the area of a sector?

Back

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

Front

How do you calculate the arc length of a sector?

Back

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

Front

What does the term 'arc length' refer to?

Back

Arc length is the distance along the curved line of a sector.

Front

What is the area of a sector?

Back

The area of a sector is the region enclosed by two radii and the arc of the circle.

Front

If the radius of a circle is 5 cm and the angle of the sector is 60 degrees, what is the arc length?

Back

Arc length = (60/360) × 2π(5) = (1/6) × 10π ≈ 5.24 cm.

Front

If the radius of a circle is 4 m and the angle of the sector is 90 degrees, what is the area of the sector?

Back

Area = (90/360) × π(4)² = (1/4) × 16π = 4π ≈ 12.57 m².

Front

What is the relationship between the angle of a sector and its area?

Back

The area of a sector is directly proportional to the angle of the sector.

Front

What is the relationship between the angle of a sector and its arc length?

Back

The arc length of a sector is directly proportional to the angle of the sector.

Front

How do you convert radians to degrees for a sector?

Back

Degrees = Radians × (180/π).

Front

What is the formula for finding the area of a segment of a circle?

Back

Area of a segment = Area of sector - Area of triangle.