A hollow copper pipe is 22 cm long and its external diameter is 28 cm.If the thickness of the pipe is 3 cm and iron weighs 8.5 g/`cm^3` , then the weight of the pipe is closest to:

Options

A. 34 kg
B. 44 kg
C. 14 kg
D. 24 kg

Answer

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

### Step 1: Determine the dimensions of the pipe
- The external diameter of the pipe is given as 28 cm.
- The thickness of the pipe is 3 cm.

From the external diameter, we can find the external radius (R):
\[ R = \frac{28 \text{ cm}}{2} = 14 \text{ cm} \]

Now, we can find the internal radius (r):
\[ r = R - \text{thickness} = 14 \text{ cm} - 3 \text{ cm} = 11 \text{ cm} \]

### Step 2: 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 \( h \) is the height (or length) of the cylinder.

Given:
- Length \( h = 22 \text{ cm} \)
- External radius \( R = 14 \text{ cm} \)
- Internal radius \( r = 11 \text{ cm} \)

Now substituting the values into the formula:
\[ V = \pi \times 22 \times (14^2 - 11^2) \]

Calculating \( R^2 \) and \( r^2 \):
\[ R^2 = 14^2 = 196 \]
\[ r^2 = 11^2 = 121 \]

Now substituting these values:
\[ V = \pi \times 22 \times (196 - 121) \]
\[ V = \pi \times 22 \times 75 \]

Using \( \pi \approx \frac{22}{7} \):
\[ V = \frac{22}{7} \times 22 \times 75 \]

### Step 3: Calculate the volume
Calculating the volume:
\[ V = \frac{22 \times 22 \times 75}{7} \]
\[ V = \frac{33000}{7} \]
\[ V \approx 4714.29 \text{ cm}^3 \]

### Step 4: Calculate the weight of the pipe
The weight of the pipe can be calculated using the density of iron:
\[ \text{Weight} = \text{Volume} \times \text{Density} \]

Given the density of iron is \( 8.5 \text{ g/cm}^3 \):
\[ \text{Weight} = 4714.29 \text{ cm}^3 \times 8.5 \text{ g/cm}^3 \]
\[ \text{Weight} \approx 40070.46 \text{ g} \]

### Step 5: Convert the weight to kilograms
To convert grams to kilograms:
\[ \text{Weight in kg} = \frac{40070.46}{1000} \approx 40.07 \text{ kg} \]

### Final Answer
The weight of the pipe is closest to **40 kg**.

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