Arc Length & Sector Area

Front

What is a region bounded by two radii of a circle and their intercepted arc?

Back

Sector of a circle.

Front

If a circle has a radius of 140 feet and a jogger runs 230 feet along the track, how do you find the measure of minor arc RN?

Back

Use the formula: Arc Measure = (Arc Length / Circumference) * 360°; Circumference = 2πr.

Front

What is the formula for the area of a sector?

Back

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

Front

Calculate the area of a shaded sector of circle O with a radius of 6 inches and a central angle of 100°.

Back

Area = (100°/360°) * π(6)² ≈ 31.4 sq. in.

Front

What is the formula for arc length?

Back

Arc Length = (θ/360°) * 2πr, where θ is the central angle in degrees.

Front

Define arc length in the context of a circle.

Back

Arc length is the distance along the curved line of a circle's circumference between two points.

Front

What is the relationship between the radius and the circumference of a circle?

Back

Circumference = 2πr, where r is the radius.

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

What is the central angle of a sector?

Back

The angle formed at the center of the circle by two radii.

Front

If the radius of a circle is doubled, how does the area of the sector change?

Back

The area of the sector increases by a factor of four.