To find the volume of the rod, we can treat it as a cylinder. The formula for the volume \( V \) of a cylinder is given by:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height (or length) of the cylinder.
### Step 1: Convert the diameter to radius
The diameter of the rod is given as \( 2.5 \, \text{mm} \). To find the radius, we divide the diameter by 2.
\[
r = \frac{d}{2} = \frac{2.5 \, \text{mm}}{2} = 1.25 \, \text{mm}
\]
### Step 2: Convert the radius to centimeters
Since the length of the rod is given in centimeters, we need to convert the radius from millimeters to centimeters.
\[
1.25 \, \text{mm} = 1.25 \times 10^{-1} \, \text{cm} = 0.125 \, \text{cm}
\]
### Step 3: Identify the length of the rod
The length of the rod is given as \( 2.5 \, \text{cm} \).
### Step 4: Calculate the volume using the formula
Now we can substitute the values of \( r \) and \( h \) into the volume formula:
\[
V = \pi r^2 h
\]
Substituting the values:
\[
V = \pi (0.125 \, \text{cm})^2 (2.5 \, \text{cm})
\]
Calculating \( (0.125 \, \text{cm})^2 \):
\[
(0.125)^2 = 0.015625 \, \text{cm}^2
\]
Now substituting this back into the volume equation:
\[
V = \pi (0.015625 \, \text{cm}^2) (2.5 \, \text{cm}) = \pi (0.0390625 \, \text{cm}^3)
\]
Using \( \pi \approx 3.14 \):
\[
V \approx 3.14 \times 0.0390625 \, \text{cm}^3 \approx 0.122 \, \text{cm}^3
\]
### Step 5: Consider significant figures
The original measurements (2.5 cm and 2.5 mm) both have 3 significant figures. Therefore, the final answer for the volume must also be expressed with 3 significant figures.
Thus, rounding \( 0.122 \, \text{cm}^3 \) to 3 significant figures gives us:
\[
V \approx 0.122 \, \text{cm}^3
\]
### Final Answer
The volume of the rod, considering significant figures, is:
\[
\boxed{0.122 \, \text{cm}^3}
\]
