Find the length of an arc of circle of radius 6cm subtending an angle of `15^(@)` at the centre.

Answer

To find the length of an arc of a circle with a radius of 6 cm that subtends an angle of 15 degrees at the center, we can follow these steps:

### Step 1: Convert the angle from degrees to radians
The formula to convert degrees to radians is:
\[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \]
For our angle of \(15^\circ\):
\[ \theta = 15 \times \frac{\pi}{180} = \frac{15\pi}{180} = \frac{\pi}{12} \text{ radians} \]

### Step 2: Use the formula for the length of an arc
The formula for the length of an arc \(l\) is given by:
\[ l = r \theta \]
where \(r\) is the radius and \(\theta\) is the angle in radians.

### Step 3: Substitute the values into the formula
Here, the radius \(r = 6\) cm and \(\theta = \frac{\pi}{12}\) radians. Substituting these values into the formula:
\[ l = 6 \times \frac{\pi}{12} \]

### Step 4: Simplify the expression
Now, simplify the expression:
\[ l = \frac{6\pi}{12} = \frac{\pi}{2} \text{ cm} \]

### Final Answer
The length of the arc is:
\[ \frac{\pi}{2} \text{ cm} \]

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