arc length and area of sectors flashcardziz

Front

What is the formula for calculating the arc length of a sector?

Back

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

Front

What is the formula for calculating the area of a sector?

Back

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

Front

If the radius of a circle is 5 ft and the central angle is 60 degrees, what is the arc length?

Back

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

Front

If the radius of a circle is 4 m and the central angle is 90 degrees, what is the area of the sector?

Back

Area = (90/360) × π(4)² = 16π/9 ≈ 17.8 m².

Front

What is the relationship between the radius and the arc length in a sector?

Back

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

Front

How does the central angle affect the area of a sector?

Back

The area of a sector increases with the central angle; a larger angle results in a larger area.

Front

What is the unit of measurement for arc length?

Back

Arc length is measured in linear units such as feet, meters, or inches.

Front

What is the unit of measurement for the area of a sector?

Back

The area of a sector is measured in square units such as square feet, square meters, or square inches.

Front

If a sector has an arc length of 10.5 in and a radius of 3 in, what is the central angle?

Back

θ = (Arc Length / (2πr)) × 360 = (10.5 / (2π(3))) × 360 ≈ 60 degrees.

Front

What is the arc length of a sector with a radius of 7 cm and a central angle of 120 degrees?

Back

Arc Length = (120/360) × 2π(7) = 14.0 cm.