Arc Length and Area of a Sector

Front

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

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 of a circle?

Back

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

Front

If the radius of a circle is 10 ft and the central angle is 60 degrees, what is the arc length?

Back

Arc Length = (60/360) * 2π(10) = (1/6) * 20π = (10/3)π ft.

Front

If the radius of a circle is 5 cm and the central angle is 90 degrees, what is the area of the sector?

Back

Area of Sector = (90/360) * π(5)² = (1/4) * 25π = (25/4)π cm².

Front

What is the relationship between the arc length and the radius of a circle?

Back

The arc length is directly proportional to the radius; as the radius increases, the arc length increases for a given central angle.

Front

What is the relationship between the area of a sector and the radius of a circle?

Back

The area of a sector is directly proportional to the square of the radius; as the radius increases, the area of the sector increases quadratically.

Front

Calculate the arc length of a circle with a radius of 8 ft and a central angle of 45 degrees.

Back

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

Front

Calculate the area of a sector with a radius of 12 cm and a central angle of 120 degrees.

Back

Area of Sector = (120/360) * π(12)² = (1/3) * 144π = 48π cm².

Front

What is the unit of measurement for arc length?

Back

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

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 centimeters.