The length and the radius of a cylinder measured with a slide cllipers re found to be 4.54 cm and 1.75 cm respectively. Calculate the volume of the cylinder.

Explanation

To calculate the volume of the cylinder, we will follow these steps:

### Step 1: Identify the formula for the volume of a cylinder.
The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) (or \( l \)) is the height (or length) of the cylinder.

### Step 2: Substitute the values into the formula.
We have:
- Radius \( r = 1.75 \, \text{cm} \)
- Length \( h = 4.54 \, \text{cm} \)
- We will use \( \pi \approx 3.14 \).

Now substituting these values into the formula:
\[ V = 3.14 \times (1.75)^2 \times 4.54 \]

### Step 3: Calculate \( r^2 \).
First, calculate \( (1.75)^2 \):
\[ (1.75)^2 = 3.0625 \]

### Step 4: Substitute back into the volume formula.
Now substituting \( r^2 \) back into the volume formula:
\[ V = 3.14 \times 3.0625 \times 4.54 \]

### Step 5: Calculate the volume.
Now we calculate the volume step by step:
1. Calculate \( 3.14 \times 3.0625 \):
\[ 3.14 \times 3.0625 = 9.6075 \]
2. Now multiply this result by \( 4.54 \):
\[ 9.6075 \times 4.54 = 43.6577 \, \text{cm}^3 \]

### Step 6: Round the answer to the correct number of significant figures.
The measurements given (length and radius) both have 3 significant figures. Therefore, we round \( 43.6577 \) to 3 significant figures:
- The third significant figure is 6, and the next digit (5) rounds it up.
Thus, the final volume is:
\[ V \approx 43.7 \, \text{cm}^3 \]

### Final Answer:
The volume of the cylinder is \( 43.7 \, \text{cm}^3 \).

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