A cylindrical tube open at both ends is made of metal. The internal diameter of the tube is 11.2 cm and its length is 21 cm. The metal everywhere is 0.4 cm thick. The volume of the metal (Take` pi = (22)/(7)`) is :

Options

A. `316 cm^3`
B. `310 cm^3`
C. `306.24 cm^3`
D. `280.52 cm^3`

Answer

To find the volume of the metal in the cylindrical tube, we need to follow these steps:

### Step 1: Calculate the internal radius and external radius of the tube.
- **Internal diameter** = 11.2 cm
- **Internal radius (r)** = Internal diameter / 2 = 11.2 cm / 2 = 5.6 cm
- **Thickness of the metal** = 0.4 cm
- **External radius (R)** = Internal radius + Thickness = 5.6 cm + 0.4 cm = 6.0 cm

### Step 2: Calculate the volume of the external cylinder.
- **Height (h)** = 21 cm
- **Volume of external cylinder (V_external)** = πR²h
- Substitute R = 6.0 cm and h = 21 cm:
- V_external = (22/7) * (6.0)² * 21
- V_external = (22/7) * 36 * 21
- V_external = (22/7) * 756
- V_external = 22 * 108 = 2376 cm³

### Step 3: Calculate the volume of the internal cylinder.
- **Volume of internal cylinder (V_internal)** = πr²h
- Substitute r = 5.6 cm and h = 21 cm:
- V_internal = (22/7) * (5.6)² * 21
- V_internal = (22/7) * 31.36 * 21
- V_internal = (22/7) * 659.56
- V_internal = 22 * 94.22 = 2069.76 cm³

### Step 4: Calculate the volume of the metal.
- **Volume of metal (V_metal)** = Volume of external cylinder - Volume of internal cylinder
- V_metal = V_external - V_internal
- V_metal = 2376 cm³ - 2069.76 cm³
- V_metal = 306.24 cm³

### Final Answer:
The volume of the metal in the cylindrical tube is approximately **306.24 cm³**.

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