What is the area of cross section (in `cm^(2)`) of the wire upto two correct significant figure, if the radius of a uniform wire is `r=0.21cm`. (`pi=22/7cm^(2)`)

Explanation

To find the area of the cross-section of a wire given its radius, we can use the formula for the area of a circle:

\[ A = \pi r^2 \]

Where:
- \( A \) is the area,
- \( r \) is the radius,
- \( \pi \) is a constant (approximately 3.14, but in this case, we will use \( \frac{22}{7} \) as given).

### Step 1: Identify the given values
- Radius \( r = 0.21 \, \text{cm} \)
- \( \pi = \frac{22}{7} \)

### Step 2: Substitute the values into the area formula
Using the formula for the area of a circle, we substitute the values:

\[ A = \pi r^2 = \frac{22}{7} \times (0.21)^2 \]

### Step 3: Calculate \( (0.21)^2 \)
First, we calculate \( (0.21)^2 \):

\[ (0.21)^2 = 0.0441 \, \text{cm}^2 \]

### Step 4: Multiply by \( \pi \)
Now we substitute \( (0.21)^2 \) back into the area formula:

\[ A = \frac{22}{7} \times 0.0441 \]

### Step 5: Perform the multiplication
Calculating \( \frac{22}{7} \times 0.0441 \):

\[ A \approx 3.14 \times 0.0441 \approx 0.1386 \, \text{cm}^2 \]

### Step 6: Round to two significant figures
Now, we round \( 0.1386 \, \text{cm}^2 \) to two significant figures:

\[ A \approx 0.14 \, \text{cm}^2 \]

### Final Answer
The area of the cross-section of the wire is approximately \( 0.14 \, \text{cm}^2 \).

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