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

Answer

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

### Step 1: Identify the formula for the area of a circle
The area \( A \) of a circle is calculated using the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

### Step 2: Substitute the given radius into the formula
The radius of the wire is given as \( r = 0.16 \, \text{mm} \). We can substitute this value into the formula:
\[ A = \pi (0.16 \, \text{mm})^2 \]

### Step 3: Calculate \( r^2 \)
First, we calculate \( (0.16 \, \text{mm})^2 \):
\[ (0.16)^2 = 0.0256 \, \text{mm}^2 \]

### Step 4: Multiply by \( \pi \)
Now we multiply \( 0.0256 \, \text{mm}^2 \) by \( \pi \) (approximately \( 3.14159 \)):
\[ A = \pi \times 0.0256 \, \text{mm}^2 \approx 3.14159 \times 0.0256 \approx 0.080384 \, \text{mm}^2 \]

### Step 5: Consider significant figures
The original radius \( 0.16 \, \text{mm} \) has 2 significant figures. Therefore, our final answer for the area must also be expressed with 2 significant figures.

### Step 6: Round the area to 2 significant figures
Rounding \( 0.080384 \, \text{mm}^2 \) to 2 significant figures gives us:
\[ A \approx 0.08 \, \text{mm}^2 \]

### Final Answer
The area of cross-section of the wire, taking significant figures into consideration, is:
\[ \boxed{0.08 \, \text{mm}^2} \]

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