Arc Length and Area Sector

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

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.

Front

How do you convert radians to degrees?

Back

Degrees = Radians × (180/π).

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 10 inches and a central angle of 90 degrees?

Back

Area = (90/360) × π(10)² = 25π in² ≈ 78.54 in².

Front

Calculate the arc length of a circle with a radius of 5 feet and a central angle of 60 degrees.

Back

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

Front

What is the area of a sector with a radius of 8 meters and a central angle of 45 degrees?

Back

Area = (45/360) × π(8)² = (1/8) × 64π = 8π m² ≈ 25.13 m².

Front

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

Back

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