How many iron rods each of length 14 m and diameter 4 cm can be made out of `0.88 m^(3)` of iron ?

Answer

To solve the problem of how many iron rods can be made from a given volume of iron, we will follow these steps:

### Step 1: Understand the dimensions of the iron rod
The iron rod is cylindrical in shape. We are given:
- Length (Height) of the rod, \( h = 14 \) m
- Diameter of the rod, \( d = 4 \) cm

### Step 2: Convert the dimensions to the same units
Since the volume of iron is given in cubic meters, we need to convert the diameter and height of the rod to meters.
- Convert diameter to meters:
\[ d = 4 \text{ cm} = \frac{4}{100} \text{ m} = 0.04 \text{ m} \]
- Calculate the radius \( r \):
\[ r = \frac{d}{2} = \frac{0.04}{2} = 0.02 \text{ m} \]
- Convert height to meters:
\[ h = 14 \text{ m} \text{ (already in meters)} \]

### Step 3: Calculate the volume of one iron rod
The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
Substituting the values:
\[ V = \frac{22}{7} \times (0.02)^2 \times 14 \]
Calculating \( (0.02)^2 \):
\[ (0.02)^2 = 0.0004 \]
Now substituting back:
\[ V = \frac{22}{7} \times 0.0004 \times 14 \]
Calculating \( 0.0004 \times 14 \):
\[ 0.0004 \times 14 = 0.0056 \]
Now substituting this value into the volume formula:
\[ V = \frac{22}{7} \times 0.0056 \]
Calculating \( \frac{22 \times 0.0056}{7} \):
\[ V = \frac{0.1232}{7} \approx 0.0176 \text{ m}^3 \]

### Step 4: Calculate the number of rods that can be made
We are given the total volume of iron available:
\[ \text{Total Volume} = 0.88 \text{ m}^3 \]
Let \( n \) be the number of rods that can be made. The total volume of the rods can be expressed as:
\[ n \times V = 0.88 \]
Substituting the volume of one rod:
\[ n \times 0.0176 = 0.88 \]
Now, solving for \( n \):
\[ n = \frac{0.88}{0.0176} \approx 50 \]

### Conclusion
Therefore, the number of iron rods that can be made from \( 0.88 \text{ m}^3 \) of iron is \( 50 \).

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