Arc Length

Front

What is the formula for arc length?

Back

The arc length (L) of a circle can be calculated using the formula: L = rθ, where r is the radius and θ is the angle in radians.

Front

How do you convert degrees to radians?

Back

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

Front

What is a minor arc?

Back

A minor arc is an arc that is smaller than a semicircle, measuring less than 180 degrees.

Front

What is a major arc?

Back

A major arc is an arc that is larger than a semicircle, measuring more than 180 degrees.

Front

If the radius of a circle is 10 cm, what is the length of an arc that subtends an angle of 60 degrees?

Back

Using the formula L = rθ, first convert 60 degrees to radians: 60 × (π/180) = π/3. Then, L = 10 × (π/3) = (10π/3) cm.

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 given by the formula C = 2πr. The fraction is determined by the angle subtended by the arc.

Front

How do you find the angle in radians if you know the arc length and radius?

Back

You can find the angle in radians using the formula: θ = L/r, where L is the arc length and r is the radius.

Front

What is the circumference of a circle with a radius of 5 cm?

Back

The circumference (C) can be calculated using the formula C = 2πr. For a radius of 5 cm, C = 2π(5) = 10π cm.

Front

If an arc length is 15 cm and the radius is 3 cm, what is the angle in radians?

Back

Using the formula θ = L/r, θ = 15/3 = 5 radians.

Front

What is the formula to find the measure of an arc in degrees?

Back

The measure of an arc in degrees can be found using the formula: degrees = (arc length / circumference) × 360.