Arc Length of a Circle

Front

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

Back

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

Front

How do you convert an angle in radians to degrees?

Back

Multiply the angle in radians by (180/π).

Front

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

Back

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

Front

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

Back

The arc length also doubles.

Front

What is the measure of a full circle in degrees?

Back

360 degrees.

Front

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

Back

θ = (Arc Length / (2πr)) * 360.

Front

What is the arc length of a circle with a radius of 10 cm and an angle of 90 degrees?

Back

Arc Length = (90/360) * 2π(10) = 15.71 cm.

Front

What is the significance of the minor arc in a circle?

Back

The minor arc is the shorter arc connecting two points on the circle, measured by the smaller angle.

Front

How do you find the length of an arc given the angle in radians?

Back

Arc Length = r * θ, where θ is the angle in radians.

Front

What is the arc length of a circle with a radius of 5 inches and an angle of π/3 radians?

Back

Arc Length = 5 * (π/3) = (5π/3) inches.