The number of iron rods, each of length 7 m and diameter 2 cm that can be made out of `0.88` cubic metres of iron is `(pi=(22)/(7))`

Options

A. 300
B. 400
C. 500
D. 600

Answer

To solve the problem of how many iron rods can be made from 0.88 cubic meters 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, \( h = 7 \, \text{m} \)
- Diameter of the rod, \( d = 2 \, \text{cm} \)

### Step 2: Calculate the radius of the rod
The radius \( r \) is half of the diameter:
\[ r = \frac{d}{2} = \frac{2 \, \text{cm}}{2} = 1 \, \text{cm} \]

### Step 3: Convert the radius to meters
Since the length of the rod is given in meters, we need to convert the radius from centimeters to meters:
\[ r = 1 \, \text{cm} = \frac{1}{100} \, \text{m} = 0.01 \, \text{m} \]

### Step 4: 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:
\[ V = \pi \times (0.01 \, \text{m})^2 \times 7 \, \text{m} \]
Using \( \pi = \frac{22}{7} \):
\[ V = \frac{22}{7} \times (0.01)^2 \times 7 \]
\[ V = \frac{22}{7} \times 0.0001 \times 7 \]
The \( 7 \) in the numerator and denominator cancels out:
\[ V = 22 \times 0.0001 = 0.0022 \, \text{m}^3 \]

### Step 5: Calculate the total volume of iron available
We are given that the total volume of iron available is:
\[ \text{Total Volume} = 0.88 \, \text{m}^3 \]

### Step 6: Calculate the number of rods
To find the number of rods that can be made, we divide the total volume by the volume of one rod:
\[ \text{Number of rods} = \frac{\text{Total Volume}}{\text{Volume of one rod}} = \frac{0.88 \, \text{m}^3}{0.0022 \, \text{m}^3} \]
Calculating this gives:
\[ \text{Number of rods} = 400 \]

### Final Answer
The number of iron rods that can be made is **400**.

---