Arc Length and Sector Area

Front

What is the formula for arc length in a circle?

Back

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

Front

How do you calculate the area of a sector in a circle?

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 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

If the radius of a circle is doubled, how does the arc length change?

Back

The arc length also doubles, since it is directly proportional to the radius.

Front

What is a sector of a circle?

Back

A sector is a region bounded by two radii and the arc between them.

Front

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

Back

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

Front

What is the measure of a full circle in degrees?

Back

A full circle measures 360 degrees.

Front

If the radius of a circle is 5 units and the central angle is 90 degrees, what is the arc length?

Back

Arc Length = (90/360) * 2π(5) = 7.85 units.

Front

What is the area of a sector with a radius of 3 units and a central angle of 60 degrees?

Back

Area of Sector = (60/360) * π(3)² = 4.71 square units.

Front

What is the difference between arc length and sector area?

Back

Arc length is the distance along the curve of the circle, while sector area is the space enclosed by the two radii and the arc.