Arc Length and Area Sector

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

How do you calculate the area of a sector?

Back

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

Front

What is the relationship between the radius and the arc length?

Back

The arc length is directly proportional to the radius; as the radius increases, the arc length increases.

Front

If the radius of a circle is doubled, how does the arc length change for the same central angle?

Back

The arc length also doubles.

Front

What is the area of a sector with a radius of 10 inches and a central angle of 90°?

Back

Area = (90/360) * π * (10)² = 25π in².

Front

What is the central angle in radians for a 180° angle?

Back

The central angle in radians is π radians.

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

What is the arc length of a circle with a radius of 5 cm and a central angle of 60°?

Back

Arc Length = (60/360) * 2π(5) = (1/6) * 10π = (5/3)π cm.

Front

What is the area of a sector with a radius of 4 m and a central angle of 45°?

Back

Area = (45/360) * π * (4)² = (1/8) * 16π = 2π m².

Front

If the radius of a circle is 3 m, what is the area of the entire circle?

Back

Area = πr² = π(3)² = 9π m².