Geometry Arc Length

Front

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

Back

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

Front

How do you convert degrees to radians?

Back

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

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

If a circle has a radius of 10 and a central angle of 90 degrees, what is the length of the arc?

Back

Arc Length = (90/360) * 2π(10) = 15.7 units.

Front

What is a minor arc?

Back

A minor arc is an arc that is less than 180 degrees.

Front

What is a major arc?

Back

A major arc is an arc that is greater than 180 degrees.

Front

How do you find the length of a minor arc given the radius and central angle?

Back

Use the formula: Arc Length = (θ/360) * 2πr.

Front

What is the arc length of a circle with a radius of 5 feet and a central angle of 60 degrees?

Back

Arc Length = (60/360) * 2π(5) = 5.24 feet.

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, affecting its length.

Front

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

Back

Use the formula: Arc Length = θ * r, where θ is in radians.