Question

Find the length of an arc of a circle
which subtends an angle of 108° at the
centre, if the radius of the circle is 15
cm.
The radius of a circle is 9 cm Find the​

Answer 1

★Given:-

• An arc of a circle  subtends an angle of 108° at the  centre.
• The radius of the circle is 15 cm.

★To find:-

• Length of the arc.

★Solution:-

Converting θ to radians:

To convert from degrees to radians, we multiply the degrees by π/180° radians .

Therefore,

➺108° = 108×(π/180)radians

           = 3π/5 radians.

Using the formula,

◖l = rθ ◗

Where,

• l = length of arc
• r = radius
• θ = angle subtended

Putting values,

➺l = rθ  

➺15(3π/5)

➺ 3(3π)

➺ 9π

[π = 3.14]

➺l = 28.27cm.

Therefore,the length of the arc is 28.27.

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Know more:-

Conversions:-

↬180 degrees is equal to π radians, so to convert degrees to radians,

• radians = π/180°× degrees

↬To convert radians to degrees,

• degrees = 180°/π ×radians

↬Area of sector subtended by arc at centre:

• Area =  ½ r² θ

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