Middle School

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Consider circle Y with a radius of 3 meters and a central angle XYZ measuring 70°.

Circle Y is shown. Line segments YZ and YX are radii with lengths of 3 meters. Angle ZYX is 70 degrees.

What is the approximate length of minor arc XZ? Round to the nearest tenth of a meter.

Answer :

Any smooth curve connecting two points is called an arc. The length of the minor arc is 1.1667π meters or 3.6652 meters.

What is the Length of an Arc?

Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,

Length of an Arc = 2π×R×(θ°/360°)

where

θ is the angle, that which arc creates at the center of the circle in degree.

Given that the length of the radius of the circle is 3 meters and the central angle of ∠XYZ is 70°. Therefore, the length of the minor arc is,

Length of minor arc = Circumference of the circle × (θ/360°)

= 2 × π × Radius × (θ/360°)

= 2 × π × 3-meter × (70°/360°)

= 1.1667π meters

= 3.6652 meter

Hence, the length of the minor arc is 1.1667π meters or 3.6652 meters.

Learn more about the Length of an Arc here:

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Rewritten by : Jeany

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