Arc Length and Sector 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 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; 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 cm and a central angle of 60 degrees?

Back

Area = (60/360) × π(5)² = (1/6) × 25π ≈ 13.09 cm².

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.

Front

What is the arc length of a circle with a radius of 10 m and a central angle of 90 degrees?

Back

Arc Length = (90/360) × 2π(10) = (1/4) × 20π = 5π ≈ 15.71 m.

Front

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

Back

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

Front

Define the term 'central angle' in relation to a circle.

Back

The central angle is the angle formed at the center of the circle by two radii.