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 `l = 4pi` cm and `r = 18` cm, then find x.

Options

A. `60^@`
B. `90^@`
C. `80^@`
D. `40^@`

Answer

To solve the problem, we need to use the formula for the length of an arc of a circle:

\[ l = \frac{x}{360} \times 2 \pi r \]

Given:
- \( l = 4\pi \) cm
- \( r = 18 \) cm

We need to find the value of \( x \).

### Step-by-Step Solution:

1. **Substitute the values into the formula:**
\[ 4\pi = \frac{x}{360} \times 2\pi \times 18 \]

2. **Simplify the right side:**
- First, calculate \( 2\pi \times 18 \):
\[ 2\pi \times 18 = 36\pi \]
- Now substitute this back into the equation:
\[ 4\pi = \frac{x}{360} \times 36\pi \]

3. **Cancel \( \pi \) from both sides:**
\[ 4 = \frac{x}{360} \times 36 \]

4. **Multiply both sides by 360 to eliminate the fraction:**
\[ 4 \times 360 = x \times 36 \]
\[ 1440 = 36x \]

5. **Divide both sides by 36 to solve for \( x \):**
\[ x = \frac{1440}{36} \]

6. **Calculate \( \frac{1440}{36} \):**
- Perform the division:
\[ x = 40 \]

### Final Answer:
The value of \( x \) is \( 40 \).

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