A hollow iron pipe of 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weights `"8 g/cm"^(3)`, then the weight of the pipe is

Options

A. `3.6` kg
B. `3.696` kg
C. 36 kg
D. `36.9` kg

Answer

To find the weight of the hollow iron pipe, we will follow these steps:

### Step 1: Identify the dimensions of the pipe
- Length of the pipe (h) = 21 cm
- External diameter = 8 cm
- Thickness of the pipe = 1 cm

### Step 2: Calculate the external radius (R) and internal radius (r)
- External radius (R) = External diameter / 2 = 8 cm / 2 = 4 cm
- Internal radius (r) = External radius - Thickness = 4 cm - 1 cm = 3 cm

### Step 3: Calculate the volume of the hollow pipe
The volume \( V \) of a hollow cylinder can be calculated using the formula:
\[ V = \pi h (R^2 - r^2) \]
where:
- \( R \) is the external radius,
- \( r \) is the internal radius,
- \( h \) is the height (length) of the cylinder.

Substituting the values:
\[ V = \pi \times 21 \times (4^2 - 3^2) \]
Calculating \( 4^2 - 3^2 \):
\[ 4^2 = 16 \quad \text{and} \quad 3^2 = 9 \quad \Rightarrow \quad 4^2 - 3^2 = 16 - 9 = 7 \]
Now substituting back into the volume formula:
\[ V = \pi \times 21 \times 7 \]
Using \( \pi \approx \frac{22}{7} \):
\[ V = \frac{22}{7} \times 21 \times 7 \]
The \( 7 \) cancels out:
\[ V = 22 \times 21 = 462 \, \text{cm}^3 \]

### Step 4: Calculate the weight of the pipe
The weight \( W \) of the pipe can be calculated using the formula:
\[ W = \text{Density} \times \text{Volume} \]
Given that the density of iron is \( 8 \, \text{g/cm}^3 \):
\[ W = 8 \, \text{g/cm}^3 \times 462 \, \text{cm}^3 \]
Calculating the weight:
\[ W = 3696 \, \text{g} \]

### Step 5: Convert grams to kilograms
To convert grams to kilograms:
\[ W = \frac{3696}{1000} = 3.696 \, \text{kg} \]

### Final Answer
The weight of the hollow iron pipe is **3.696 kg**.

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