Radius of a wire is 2.50 mm. The length of the wire is 50.0 cm. If mass of wire was measured as 25g, then find the density of wire in correct significant figures.
`[Given, pi = 3.14, exact]`

Explanation

To find the density of the wire, we will follow these steps:

### Step 1: Convert the Measurements
1. **Convert the radius from mm to meters**:
\[ r = 2.50 \, \text{mm} = 2.50 \times 10^{-3} \, \text{m} \]

2. **Convert the length from cm to meters**:
\[ L = 50.0 \, \text{cm} = 50.0 \times 10^{-2} \, \text{m} = 0.50 \, \text{m} \]

3. **Convert the mass from grams to kilograms**:
\[ m = 25 \, \text{g} = 25 \times 10^{-3} \, \text{kg} = 0.025 \, \text{kg} \]

### Step 2: Calculate the Volume of the Wire
The volume \( V \) of the wire can be calculated using the formula for the volume of a cylinder:
\[ V = \pi r^2 L \]
Substituting the values:
\[ V = 3.14 \times (2.50 \times 10^{-3})^2 \times 0.50 \]
Calculating \( r^2 \):
\[ (2.50 \times 10^{-3})^2 = 6.25 \times 10^{-6} \, \text{m}^2 \]
Now substituting this back into the volume formula:
\[ V = 3.14 \times 6.25 \times 10^{-6} \times 0.50 \]
Calculating:
\[ V = 3.14 \times 3.125 \times 10^{-6} = 9.8125 \times 10^{-6} \, \text{m}^3 \]

### Step 3: Calculate the Density of the Wire
Now, we can find the density \( \rho \) using the formula:
\[ \rho = \frac{m}{V} \]
Substituting the values:
\[ \rho = \frac{0.025 \, \text{kg}}{9.8125 \times 10^{-6} \, \text{m}^3} \]
Calculating:
\[ \rho = 2547.770701 \, \text{kg/m}^3 \]

### Step 4: Round to Correct Significant Figures
The values given in the problem have the following significant figures:
- Radius: 2.50 mm (3 significant figures)
- Length: 50.0 cm (3 significant figures)
- Mass: 25 g (2 significant figures)

The least number of significant figures is 2 (from mass). Therefore, we round the density to 2 significant figures:
\[ \rho \approx 2500 \, \text{kg/m}^3 \]

### Final Answer
The density of the wire is \( \rho = 2500 \, \text{kg/m}^3 \).

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