A hollow iron pipe is 28 cm long and its external diameter is 10 cm.If the thickness of the pipe is 2 cm and iron weighs `5g//cm^(3)`, then the weight of the pipe is :

Options

A. 70.4 kg
B. 7.04 kg
C. 74 kg
D. 7.40 kg

Answer

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

### Step 1: Determine the external and internal diameters
- The external diameter of the pipe is given as 10 cm.
- The thickness of the pipe is 2 cm, which means the internal diameter can be calculated as:
\[ \text{Internal Diameter} = \text{External Diameter} - 2 \times \text{Thickness} = 10 \, \text{cm} - 2 \times 2 \, \text{cm} = 6 \, \text{cm} \]

### Step 2: Calculate the external and internal radii
- The external radius \( R_e \) is half of the external diameter:
\[ R_e = \frac{10 \, \text{cm}}{2} = 5 \, \text{cm} \]
- The internal radius \( R_i \) is half of the internal diameter:
\[ R_i = \frac{6 \, \text{cm}}{2} = 3 \, \text{cm} \]

### Step 3: Calculate the volume of the hollow pipe
- The volume \( V \) of the hollow pipe can be calculated using the formula:
\[ V = \pi (R_e^2 - R_i^2) \times h \]
where \( h \) is the height (length) of the pipe, which is 28 cm.
- Substituting the values:
\[ V = \pi (5^2 - 3^2) \times 28 \]
\[ = \pi (25 - 9) \times 28 \]
\[ = \pi \times 16 \times 28 \]
\[ = 448\pi \, \text{cm}^3 \]
(Using \( \pi \approx 3.14 \), we can approximate this to \( 448 \times 3.14 \approx 1408 \, \text{cm}^3 \))

### Step 4: Calculate the weight of the pipe
- The weight \( W \) of the pipe can be calculated using the formula:
\[ W = V \times \text{Density} \]
where the density of iron is given as \( 5 \, \text{g/cm}^3 \).
- Substituting the values:
\[ W = 1408 \, \text{cm}^3 \times 5 \, \text{g/cm}^3 = 7040 \, \text{g} \]
- Converting grams to kilograms:
\[ W = \frac{7040 \, \text{g}}{1000} = 7.04 \, \text{kg} \]

### Final Answer
The weight of the hollow iron pipe is **7.04 kg**.

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