Anjali has 0.88 cubic metres of iron. Find the number of cylindrical iron rods, each of length 14 m and diameter 2 cm, she can make.

Options

A. 150
B. 200
C. 250
D. 400

Answer

To find the number of cylindrical iron rods Anjali can make from 0.88 cubic meters of iron, we will follow these steps:

### Step 1: Calculate the volume of one cylindrical iron rod.
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.

### Step 2: Convert the dimensions of the rod to the same unit.
The length of the rod is given as 14 meters, and the diameter is 2 cm. We need to convert the diameter to meters to match the length.

\[ \text{Diameter} = 2 \text{ cm} = \frac{2}{100} \text{ m} = 0.02 \text{ m} \]

Now, we can find the radius:

\[ r = \frac{\text{Diameter}}{2} = \frac{0.02}{2} = 0.01 \text{ m} \]

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

\[ V = \pi (0.01)^2 (14) \]

Using \( \pi \approx \frac{22}{7} \):

\[ V = \frac{22}{7} \times (0.01)^2 \times 14 \]

### Step 4: Simplify the expression.
Calculating \( (0.01)^2 \):

\[ (0.01)^2 = 0.0001 \]

Now substituting this back into the volume formula:

\[ V = \frac{22}{7} \times 0.0001 \times 14 \]

### Step 5: Calculate the volume.
Now, we can calculate the volume:

\[ V = \frac{22 \times 0.0001 \times 14}{7} \]

Calculating \( 22 \times 14 = 308 \):

\[ V = \frac{308 \times 0.0001}{7} = \frac{0.0308}{7} \approx 0.0044 \text{ m}^3 \]

### Step 6: Calculate the number of rods.
To find the number of rods, we divide the total volume of iron by the volume of one rod:

\[ \text{Number of rods} = \frac{0.88}{0.0044} \]

Calculating this gives:

\[ \text{Number of rods} = 200 \]

### Final Answer:
Anjali can make **200 cylindrical iron rods**.

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