Arc Lengths

Front

What is the formula to find 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 a central angle in a circle.

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides are radii that extend to the circle.

Front

If the radius of a circle is 5 and the central angle is 90 degrees, what is the arc length?

Back

Arc Length = (90/360) * 2π(5) = (1/4) * 10π = 2.5π.

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 for a given central angle.

Front

How do you convert degrees to radians?

Back

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

Front

Find the arc length of a circle with a radius of 3 inches and a central angle of 60 degrees.

Back

Arc Length = (60/360) * 2π(3) = (1/6) * 6π = π inches.

Front

What is the measure of a minor arc?

Back

A minor arc is the shorter arc connecting two points on a circle, measured in degrees.

Front

If the radius of a circle is 10 and the minor arc AB measures 120 degrees, what is the length of arc AB?

Back

Arc Length = (120/360) * 2π(10) = (1/3) * 20π = (20/3)π.

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.

Front

How do you find the length of an arc in terms of π?

Back

Use the formula: Arc Length = (θ/360) * 2πr, and leave the answer in terms of π.