Arc Length WorkStation

Front

What is the formula for arc length?

Back

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

Front

What does the term 'arc length' refer to?

Back

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

Front

How do you calculate the arc length of a sector with a central angle of 60 degrees and a radius of 5 units?

Back

Arc Length = (60/360) × 2π(5) = (1/6) × 10π ≈ 5.24 units.

Front

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

Back

Arc length increases with an increase in the radius, assuming the angle remains constant.

Front

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

Back

The arc length also doubles if the radius is doubled, as arc length is directly proportional to the radius.

Front

What is the unit of measurement for arc length?

Back

Arc length is measured in linear units, such as centimeters, meters, inches, etc.

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 find the area of a sector?

Back

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

Front

What is the difference between arc length and the chord length?

Back

Arc length is the distance along the curve, while chord length is the straight line distance between the endpoints of the arc.

Front

If the arc length is 10 units and the radius is 5 units, what is the central angle in degrees?

Back

θ = (Arc Length / (2πr)) × 360 = (10 / (2π(5))) × 360 = 114.6 degrees.