Sectors: Arc Length and Area (Updated)

Front

What is the formula for the area of a sector?

Back

Area = (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 'sector' refer to in geometry?

Back

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

Front

If the radius of a sector is 5 m and the angle is 60 degrees, what is the area of the sector?

Back

Area = (60/360) × π(5)² = 13.09 m² (approximately).

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; larger angles yield larger areas.

Front

How do you convert radians to degrees for sector calculations?

Back

Degrees = Radians × (180/π).

Front

What is the area of a sector with a radius of 10 cm and an angle of 90 degrees?

Back

Area = (90/360) × π(10)² = 78.54 cm² (approximately).

Front

What is the arc length of a sector with a radius of 4 m and an angle of 45 degrees?

Back

Arc Length = (45/360) × 2π(4) = 3.14 m (approximately).

Front

If a sector has an area of 25 m² and a radius of 5 m, what is the angle in degrees?

Back

θ = (Area × 360) / (πr²) = (25 × 360) / (π(5)²) = 72 degrees (approximately).

Front

What is the formula to find the radius of a sector if the area and angle are known?

Back

Radius = √(Area × (360)/(πθ)).