Arc Length

Front

What is the formula for calculating arc length?

Back

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

Front

Define 'arc' in the context of a circle.

Back

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

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

How do you convert degrees to radians?

Back

To convert degrees to radians, multiply by π/180.

Front

If the radius of a circle is 10 cm and the central angle is 60 degrees, what is the arc length?

Back

Arc Length = (60/360) * 2π(10) = 10.47 cm.

Front

What is the unit of measurement for arc length?

Back

Arc length can be measured in any linear unit, such as meters, centimeters, inches, etc.

Front

How does the radius affect the arc length?

Back

A larger radius results in a longer arc length for the same central angle.

Front

What is the difference between a minor arc and a major arc?

Back

A minor arc is less than 180 degrees, while a major arc is more than 180 degrees.

Front

If an arc length is 5 m and the radius is 2 m, what is the central angle in degrees?

Back

θ = (Arc Length / (2πr)) * 360 = (5 / (2π(2))) * 360 = 39.79 degrees.

Front

What is the circumference of a circle?

Back

Circumference = 2πr, where r is the radius.