WARM-UP: Central Angles, Arc, Arc Length, and Sector Area

Front

What is a central angle?

Back

A central angle is an angle whose vertex is at the center of a circle and whose sides are radii that extend to the circumference.

Front

What is a sector in a circle?

Back

A sector is a portion of a circle enclosed by two radii and the arc between them.

Front

How do you calculate the area of a sector?

Back

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

Front

What is an arc in a circle?

Back

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

Front

How do you find the length of an arc?

Back

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

Front

What is the formula for the area of a circle?

Back

Area of a circle = πr², where r is the radius.

Front

What is the relationship between the central angle and the arc length?

Back

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

Front

What is the measure of a full circle in degrees?

Back

A full circle measures 360 degrees.

Front

If the central angle is 90 degrees, what fraction of the circle does the sector represent?

Back

The sector represents 1/4 of the circle.

Front

What is the difference between a sector and a segment?

Back

A sector is enclosed by two radii and an arc, while a segment is enclosed by a chord and an arc.