The thickness of a metallic tube is 1 cm and its outer radius is 11 cm. Find the mass of such 1 metre a long tube, if the density of the metal is 7.5 g per `cm^3`. `[ "Take" pi =(22)/(7) ]`

Answer

To solve the problem, we need to find the mass of a metallic tube with given dimensions and density. Here are the steps to arrive at the solution:

### Step 1: Identify the given values
- Thickness of the tube (t) = 1 cm
- Outer radius (R) = 11 cm
- Length of the tube (h) = 1 m = 100 cm (since we need to work in cm)
- Density of the metal (ρ) = 7.5 g/cm³

### Step 2: Calculate the inner radius (r)
The inner radius can be calculated by subtracting the thickness from the outer radius:
\[ r = R - t = 11 \, \text{cm} - 1 \, \text{cm} = 10 \, \text{cm} \]

### Step 3: Calculate the volume of the hollow tube
The volume \( V \) of the hollow tube can be found using the formula for the volume of a cylinder:
\[ V = \pi h (R^2 - r^2) \]
Substituting the values:
\[ V = \frac{22}{7} \times 100 \, \text{cm} \times (11^2 - 10^2) \]
Calculating \( 11^2 \) and \( 10^2 \):
\[ 11^2 = 121 \quad \text{and} \quad 10^2 = 100 \]
Thus,
\[ V = \frac{22}{7} \times 100 \times (121 - 100) = \frac{22}{7} \times 100 \times 21 \]
Calculating further:
\[ V = \frac{22 \times 100 \times 21}{7} = \frac{46200}{7} = 6600 \, \text{cm}^3 \]

### Step 4: Calculate the mass of the tube
Using the formula for mass:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
Substituting the values:
\[ \text{Mass} = 7.5 \, \text{g/cm}^3 \times 6600 \, \text{cm}^3 \]
Calculating the mass:
\[ \text{Mass} = 49500 \, \text{g} = 49.5 \, \text{kg} \]

### Final Answer
The mass of the 1-meter-long metallic tube is **49.5 kg**.