Arc Length and Sector Area

Front

What is the formula for calculating the length of an arc?

Back

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

Front

Define 'central angle' in the context of a circle.

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides intersect the circle.

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 10 cm and the central angle is 60 degrees, what is the length of the arc?

Back

Length of arc = (60/360) × 2π(10) = (1/6) × 20π = (10/3)π cm.

Front

What is the area of a sector with a radius of 5 cm and a central angle of 90 degrees?

Back

Area of sector = (90/360) × π(5)² = (1/4) × 25π = 6.25π cm².

Front

What is an arc in a circle?

Back

An arc is a portion of the circumference of a circle.

Front

How do you find the measure of an arc given the central angle?

Back

The measure of the arc in degrees is equal to the measure of the central angle.

Front

What is the difference between a sector and a segment in a circle?

Back

A sector is the area enclosed by two radii and the arc, while a segment is the area between a chord and the arc.

Front

If the length of an arc is 44 cm and the radius is 14 cm, what is the central angle?

Back

θ = (Length of arc / (2πr)) × 360 = (44 / (2π(14))) × 360 = 45 degrees.