Sectors: Arc Length and Area

Front

What is the formula for the area of a sector?

Back

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

Front

What is the formula for the arc length of a sector?

Back

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

Front

Define 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 the relationship between the central angle and the area of a sector?

Back

The area of a sector is directly proportional to the central angle; as the angle increases, the area increases.

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

What is the area of a sector with a radius of 5 m and a central angle of 60 degrees?

Back

Area = (60/360) × π(5)² = (1/6) × 25π ≈ 13.1 m².

Front

If the radius of a sector is doubled, how does the area change?

Back

The area increases by a factor of four, since area is proportional to the square of the radius.

Front

What is the arc length of a sector with a radius of 4 m and a central angle of 90 degrees?

Back

Arc Length = (90/360) × 2π(4) = (1/4) × 8π = 2π ≈ 6.3 m.

Front

What is the area of a sector with a radius of 10 units and a central angle of 45 degrees?

Back

Area = (45/360) × π(10)² = (1/8) × 100π ≈ 39.3 units².

Front

How do you find the central angle if you know the area of the sector and the radius?

Back

θ = (Area × 360) / (πr²).