Directions for questions : These questions are based on the following information.
The length of an arc of a circle is given by the formula `l = (x)/( 360^@) xx 2 pi r`.
If `x = 60^(@) and r =3 "cm"`, then find `l`.

Options

A. 22 cm
B. `2pi` cm
C. `pi` cm
D. 11 cm

Answer

To find the length of the arc (l) using the given formula, we will follow these steps:

### Step 1: Write down the formula for the length of an arc.
The formula for the length of an arc is given by:
\[ l = \frac{x}{360^\circ} \times 2 \pi r \]

### Step 2: Substitute the values of \( x \) and \( r \).
We are given:
- \( x = 60^\circ \)
- \( r = 3 \, \text{cm} \)

Now, substitute these values into the formula:
\[ l = \frac{60}{360} \times 2 \pi \times 3 \]

### Step 3: Simplify the fraction.
Calculate \( \frac{60}{360} \):
\[ \frac{60}{360} = \frac{1}{6} \]

Now, substitute this back into the equation:
\[ l = \frac{1}{6} \times 2 \pi \times 3 \]

### Step 4: Calculate \( 2 \pi \times 3 \).
Now, calculate \( 2 \pi \times 3 \):
\[ 2 \pi \times 3 = 6 \pi \]

### Step 5: Substitute back into the equation.
Now substitute this back into the equation for \( l \):
\[ l = \frac{1}{6} \times 6 \pi \]

### Step 6: Simplify the equation.
The \( 6 \) in the numerator and denominator cancels out:
\[ l = \pi \]

### Step 7: Calculate the numerical value of \( l \).
Using \( \pi \approx 3.14 \):
\[ l \approx 3.14 \, \text{cm} \]

### Conclusion:
Thus, the length of the arc \( l \) is approximately \( 3.14 \, \text{cm} \).

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