The inner radius of a pipe is 2.1 cm. How much water can 12 m of this pipe hold ?

Answer

To find out how much water a pipe can hold, we need to calculate the volume of the cylindrical part of the pipe. Here’s how to do it step by step:

### Step 1: Understand the dimensions
The inner radius of the pipe is given as 2.1 cm, and the length of the pipe is 12 m.

### Step 2: Convert the length from meters to centimeters
Since the radius is in centimeters, we need to convert the length of the pipe from meters to centimeters:
\[ 12 \text{ m} = 12 \times 100 = 1200 \text{ cm} \]

### Step 3: Use 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 \( h \) is the height (or length in this case).

### Step 4: Substitute the values into the formula
Here, \( r = 2.1 \) cm and \( h = 1200 \) cm. We will use \( \pi \approx \frac{22}{7} \):
\[ V = \frac{22}{7} \times (2.1)^2 \times 1200 \]

### Step 5: Calculate \( (2.1)^2 \)
First, calculate \( (2.1)^2 \):
\[ (2.1)^2 = 4.41 \]

### Step 6: Substitute \( (2.1)^2 \) back into the volume formula
Now substitute \( 4.41 \) back into the volume formula:
\[ V = \frac{22}{7} \times 4.41 \times 1200 \]

### Step 7: Simplify the calculation
To make calculations easier, convert \( 4.41 \) into a fraction:
\[ 4.41 = \frac{441}{100} \]
So now the volume becomes:
\[ V = \frac{22}{7} \times \frac{441}{100} \times 1200 \]

### Step 8: Calculate \( \frac{22 \times 441 \times 1200}{7 \times 100} \)
Now calculate the numerator and denominator:
1. Calculate \( 22 \times 441 = 9702 \)
2. Calculate \( 9702 \times 1200 = 11642400 \)
3. Calculate \( 7 \times 100 = 700 \)

So now we have:
\[ V = \frac{11642400}{700} \]

### Step 9: Simplify the fraction
Now simplify \( \frac{11642400}{700} \):
\[ V = 16632 \text{ cm}^3 \]

### Step 10: Convert cubic centimeters to liters
Since \( 1 \text{ liter} = 1000 \text{ cm}^3 \), we convert the volume into liters:
\[ V = \frac{16632}{1000} = 16.632 \text{ liters} \]

### Final Answer
The amount of water that the pipe can hold is **16.632 liters**.

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