Any smooth curve connecting two points is called an arc. The length of arc XPY is 9π cm.
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 centre of the circle in degree.
A circle has 360°, while the angle made by arc XY is 90°. Therefore, the measure of the angle made by the arc XPY at the centre of the circle is 270°. Also, the radius of the circle is 6 cm, therefore, the length of XPY is,
Length of XPY = 2π×6cm×(270°/360°) = 9π cm
Hence, the length of arc XPY is 28.2743 cm.
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