Sector Area and Arc Length

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 arc length?

Back

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

Front

What does 'sector' mean in geometry?

Back

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

Front

How do you find the area of a circle?

Back

Area = πr², where r is the radius of the circle.

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; larger angles result in larger areas.

Front

If the radius of a circle is 5 cm, what is the area of the circle?

Back

Area = π(5)² = 25π ≈ 78.54 cm².

Front

What is the central angle of a full circle?

Back

The central angle of a full circle is 360 degrees.

Front

How do you convert radians to degrees?

Back

Degrees = Radians × (180/π).

Front

What is the area of a sector with a radius of 4 cm and a central angle of 90 degrees?

Back

Area = (90/360) × π(4)² = (1/4) × 16π = 4π ≈ 12.57 cm².

Front

What is the arc length of a sector with a radius of 3 m and a central angle of 60 degrees?

Back

Arc Length = (60/360) × 2π(3) = (1/6) × 6π = π ≈ 3.14 m.