Arc Length

Front

What is the formula for calculating the arc length of a circle?

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 radius and the arc length?

Back

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

Front

How do you convert degrees to radians for arc length calculations?

Back

To convert degrees to radians, use the formula: radians = degrees × (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) = (1/6) × 20π ≈ 10.47 cm.

Front

What is the significance of the central angle in determining arc length?

Back

The central angle determines the fraction of the circle's circumference that the arc represents.

Front

How does the unit of measurement affect arc length calculations?

Back

Arc length must be calculated using consistent units; if the radius is in cm, the arc length will also be in cm.

Front

What is a semicircle and how does it relate to arc length?

Back

A semicircle is an arc that represents half of a circle, with a central angle of 180 degrees.

Front

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

Back

Using the formula: θ = (Arc Length / (2πr)) × 360, θ = (5 / (2π(2))) × 360 ≈ 45 degrees.

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 greater than 180 degrees.