The length of arc AB is 3π given that radius of the circle is 27 units and the angle made by the arc AB at the center of the circle is 20°. This can be obtained using the formula to find arc length.
Find the length of the arc AB:
Formula used for finding arc length:
- If the angle made by the arc at the center of the circle is in degrees, the formula to find the length of the arc is,
⇒ L = 2 π r (θ/360°)
where r is the radius of the circle and θ is the angle made by the arc at the center of the circle.
- If the angle made by the arc at the center of the circle is in radians, the formula to find the length of the arc is,
⇒ L = r × θ
where r is the radius of the circle and θ is the angle made by the arc at the center of the circle.
Here in the question it is given that,
r = 27 units
θ = 20°
Since the angle made by the arc at the center of the circle is in degrees, the formula to find the length of the arc is,
⇒ L = 2 π r (θ/360°)
L = 2 π (27) (20°/360°)
L = π (27) (20°/180°)
⇒ L = 3 π
Hence the length of arc AB is 3 π given that radius of the circle is 27 units and the angle made by the arc AB at the center of the circle is 20°.
Learn more about arc length here:
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