Arc Length

Front

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

Back

The length of an arc (L) can be calculated using the formula: L = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius of the circle.

Front

How do you convert degrees to radians when calculating arc length?

Back

To convert degrees to radians, use the formula: radians = degrees × (π/180).

Front

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

Back

The length of an arc is directly proportional to the radius of the circle; as the radius increases, the length of the arc also increases.

Front

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

Back

The central angle determines the proportion of the circle that the arc represents; a larger central angle results in a longer arc.

Front

If the radius of a circle is doubled, how does that affect the length of an arc?

Back

If the radius is doubled, the length of the arc also doubles, assuming the central angle remains the same.

Front

What units are typically used to express arc length?

Back

Arc length can be expressed in any linear unit, such as inches, feet, meters, or miles, depending on the context.

Front

How do you find the arc length if the central angle is given in radians?

Back

If the central angle is in radians, the arc length can be calculated using the formula: L = rθ, where r is the radius and θ is the angle in radians.

Front

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

Back

The arc length is a fraction of the circumference of the circle, which is calculated as C = 2πr. The fraction is determined by the central angle.

Front

How can you find the central angle if you know the arc length and radius?

Back

The central angle in radians can be found using the formula: θ = L/r, where L is the arc length and r is the radius.

Front

What is the formula for the circumference of a circle?

Back

The circumference (C) of a circle is calculated using the formula: C = 2πr, where r is the radius.