How many cubic metres of water fill a pipe which is 3500 m long and 0.08 m in diamter ?

Options

A. `17.5 m^(3) `
B. `17.6 m^(3) `
C. `21 m^(3) `
D. `35 m^(3) `

Answer

To find out how many cubic meters of water can fill a cylindrical pipe, we need to calculate the volume of the 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,
- \( \pi \) is a constant approximately equal to \( \frac{22}{7} \) or \( 3.14 \).

### Step 1: Find the radius of the pipe
The diameter of the pipe is given as \( 0.08 \) m. The radius \( r \) can be calculated as:

\[ r = \frac{\text{diameter}}{2} = \frac{0.08}{2} = 0.04 \text{ m} \]

### Step 2: Identify the height of the pipe
The height \( h \) of the pipe is given as \( 3500 \) m.

### Step 3: Substitute the values into the volume formula
Now we can substitute the values of \( r \) and \( h \) into the volume formula:

\[ V = \pi r^2 h = \frac{22}{7} \times (0.04)^2 \times 3500 \]

### Step 4: Calculate \( r^2 \)
First, calculate \( r^2 \):

\[ r^2 = (0.04)^2 = 0.0016 \]

### Step 5: Substitute \( r^2 \) back into the volume formula
Now substitute \( r^2 \) back into the volume formula:

\[ V = \frac{22}{7} \times 0.0016 \times 3500 \]

### Step 6: Simplify the calculation
Now, we can simplify the calculation step-by-step:

1. Calculate \( 0.0016 \times 3500 \):

\[ 0.0016 \times 3500 = 5.6 \]

2. Now substitute this back into the volume formula:

\[ V = \frac{22}{7} \times 5.6 \]

3. Calculate \( \frac{22 \times 5.6}{7} \):

\[ 22 \times 5.6 = 123.2 \]

4. Now divide by \( 7 \):

\[ V = \frac{123.2}{7} = 17.6 \]

### Final Answer
Thus, the volume of water that can fill the pipe is:

\[ \boxed{17.6} \text{ cubic meters} \]