The radius of a thin wire is `0.16mm`. The area of cross section taking significant figures into consideration in square millimeter is

Options

A. 0.08
B. `0.080`
C. `0.0804`
D. `0.080384`

Explanation

To find the area of cross-section of a thin wire given its radius, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given radius**: The radius of the thin wire is given as \( r = 0.16 \, \text{mm} \).

2. **Use the formula for the area of a circle**: The area \( A \) of the cross-section of the wire can be calculated using the formula:
\[ A = \pi r^2 \]

3. **Substitute the radius into the formula**: Plugging in the value of the radius:
\[ A = \pi (0.16 \, \text{mm})^2 \]

4. **Calculate \( r^2 \)**: First, calculate \( 0.16^2 \):
\[ 0.16^2 = 0.0256 \, \text{mm}^2 \]

5. **Multiply by \( \pi \)**: Now, multiply by \( \pi \) (approximately \( 3.14159 \)):
\[ A \approx 3.14159 \times 0.0256 \approx 0.080384 \, \text{mm}^2 \]

6. **Determine significant figures**: The radius \( 0.16 \, \text{mm} \) has 2 significant figures. Therefore, the area must also be expressed with 2 significant figures.

7. **Round the area**: The calculated area \( 0.080384 \, \text{mm}^2 \) needs to be rounded to 2 significant figures:
- The first rounding gives \( 0.08038 \, \text{mm}^2 \) (still 5 significant figures).
- The second rounding gives \( 0.0804 \, \text{mm}^2 \) (now 4 significant figures).
- The final rounding gives \( 0.080 \, \text{mm}^2 \) (which has 2 significant figures).

8. **Final answer**: The area of cross-section taking significant figures into consideration is:
\[ A \approx 0.080 \, \text{mm}^2 \]