Arc Length and Sector Area

Front

What is the formula for arc length in a circle?

Back

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

Front

What is the formula for the area of a sector in a circle?

Back

Area of Sector = (θ/360) * πr², where θ is the angle in degrees and r is the radius.

Front

If a circle has a radius of 10 cm, what is the circumference?

Back

Circumference = 2πr = 2π(10) = 20π cm.

Front

What is the relationship between the angle of a sector and the arc length?

Back

The arc length is directly proportional to the angle of the sector.

Front

How do you find the radius if you know the arc length and the angle?

Back

Rearrange the arc length formula: r = (Arc Length * 360) / (2πθ).

Front

What is the area of a circle with a radius of 5 inches?

Back

Area = πr² = π(5)² = 25π square inches.

Front

If a sector has an area of 32π in² and an angle of 90°, what is the radius?

Back

Radius = √(Area / (π/4)) = √(32π / (π/4)) = √(128) = 16 in.

Front

What is the measure of a 45° arc in a circle with a radius of 8 inches?

Back

Arc Length = (45/360) * 2π(8) = (1/8) * 16π = 2π inches.

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 cm and an angle of 60°?

Back

Area = (60/360) * π(10)² = (1/6) * 100π = (50/3)π cm².