Arc Length Formula

Arc Length Formula

Length=θ°360°2πr

The arc length formula is used to find the length of an arc of a circle. An arc is a part of the circumference of a circle.

Again, when working with π, if we want an exact answer, we use π. If we want to approximate an answer, we substitute a rounded form of π, such as 3.14.Also, r refers to the radius of the circle which is the distance from the center to circumference of a circle. The symbol theta, θ, is used for angle degree measures.

Example 1:

Find the arc length of an arc formed by 60° of a circle with a radius of 8 inches.

Step 1:

Find the variables.

θ = 60°

r=8

Step 2:

Substitute into formula.

Length=60°360°2π(8)

Step 3:

Evaluate for Arc Length

Length=16π6

Length=8π3

If you want an approximate answer, use 3.14

Length=8(3.14)3

Length =8.37

Answer:

The length is about 8.37 inches.

Example 2:

Find the arc length of an arc formed by 75° of a circle with a diameter of 18cm.

Step 1:

Find the variables.

θ = 75°

r = 9 since that is half of the diameter.

Step 2:

Substitute into formula.

Length=75°360°2π(9)

Step 3:

Evaluate for Arc Length

Length=7518π360

Length=15π4

If you want an approximate answer, use 3.14

Length=15(3.14)4

Length = 11.78

Answer:

The length is about 11.78 inches.

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