Arc Length and Sector Area

Front

What is the formula for the arc length of 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 of a circle?

Back

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

Front

If the radius of a circle is 10 cm and the angle is 90°, what is the area of the sector?

Back

Area of Sector = (90/360) × π(10)² = 78.54 cm².

Front

If the radius of a circle is 5 cm and the angle is 60°, what is the arc length?

Back

Arc Length = (60/360) × 2π(5) = 5.24 cm.

Front

What is the relationship between the angle in degrees and the arc length?

Back

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

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 circle with a radius of 7 cm?

Back

Area = πr² = π(7)² = 153.94 cm².

Front

If a circle has a radius of 4 cm, what is the circumference?

Back

Circumference = 2πr = 2π(4) = 25.13 cm.

Front

What is the area of a sector with a radius of 3 cm and an angle of 120°?

Back

Area of Sector = (120/360) × π(3)² = 9.42 cm².