How to find the length of an arc, formula | example.

An arc is any part of the circumference of a circle. The length of an arc is the distance measured along the arc. The circumference of a circle is the circular part of the circle. The circumference is the perimeter of a circle. On this page, we will discuss the length of a minor arc in detail.

How to find the length of an arc.

The length of an arc is any distance measured on the circumference of a circle. The length of an arc is found by multiplying the theta (θ) over the total area of a circle (360°) with the circumference of the circle. i.e length of an arc is = θ/360° × circumference of a circle. The formula for finding the circumference of a circle is = 2πr. So, the length of an arc is = θ/360° × 2πr

Note: θ is the angle of the sector of the circle. The sector of a circle is the area bounded by two radii (radii).

let’s understand the length of an arc by working through some examples.

Example 1. Find the length of an arc given that the radius of the circle is 7cm and the angle of sector AOB is 60°. [Take π=22/7]

Solution

The length of an arc is = θ/360° × 2πr, where θ = 60°, π = 22/7, and the radius = 7cm

= 60°/360° × 2 × 22/7 × 7cm

= 1/6 × 44/7 × 7, ( since 60°/360°=1/6 and 2×22=44)

=1/6×44, ( since 44/7 × 7 = 44)

= 44/6

= 7.3cm

∴ the length of the arc is 7.3cm.

Example 2. A is the center of the circle with a radius of 20cm. If the angle BAC is 90° where AB and AC are radii of the circle. Find the length of the arc BC.

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Solution

Length of an arc = θ/360° × 2πr, where θ = 90°, π = 22/7, and radius = 20cm.

= 90/360 × 2 × 22/7 × 20

= 1/4 × 40×22/7

= 880/28

= 31.4cm

∴ The length of the arc BC = 31.4cm.

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