A hollow cylindrical tube open at both ends is made of iron 2 cm thick. If the external diameter be 50 cm and the length of the tube is 210 cm, find the volume

Options

A. a.63360
B. b.500000
C. c.379500
D. d. none

Answer

To find the volume of the hollow cylindrical tube, we can follow these steps:

### Step 1: Identify the given values
- External diameter of the tube = 50 cm
- Thickness of the tube = 2 cm
- Length (height) of the tube = 210 cm

### Step 2: Calculate the external radius
The external radius (R) is half of the external diameter:
\[ R = \frac{\text{External diameter}}{2} = \frac{50 \text{ cm}}{2} = 25 \text{ cm} \]

### Step 3: Calculate the internal radius
The internal radius (r) can be found by subtracting the thickness from the external radius:
\[ r = R - \text{Thickness} = 25 \text{ cm} - 2 \text{ cm} = 23 \text{ cm} \]

### Step 4: Use the formula for the volume of a hollow cylinder
The volume \( V \) of a hollow cylinder is given by the formula:
\[ V = \pi h (R^2 - r^2) \]
Where:
- \( h \) is the height (length) of the cylinder,
- \( R \) is the external radius,
- \( r \) is the internal radius.

### Step 5: Substitute the values into the formula
Substituting the values we have:
\[ V = \pi \times 210 \times (25^2 - 23^2) \]

### Step 6: Calculate \( R^2 \) and \( r^2 \)
Calculating the squares:
\[ 25^2 = 625 \]
\[ 23^2 = 529 \]
Now, find \( R^2 - r^2 \):
\[ R^2 - r^2 = 625 - 529 = 96 \]

### Step 7: Substitute back into the volume formula
Now substitute back into the volume formula:
\[ V = \pi \times 210 \times 96 \]

### Step 8: Use the value of \( \pi \)
Using \( \pi \approx \frac{22}{7} \):
\[ V = \frac{22}{7} \times 210 \times 96 \]

### Step 9: Simplify the expression
First, simplify \( \frac{210}{7} \):
\[ \frac{210}{7} = 30 \]
Now, substitute this back:
\[ V = 22 \times 30 \times 96 \]

### Step 10: Calculate the final volume
Now, calculate \( 22 \times 30 \times 96 \):
\[ 22 \times 30 = 660 \]
\[ 660 \times 96 = 63360 \]

### Final Answer
The volume of the hollow cylindrical tube is:
\[ \text{Volume} = 63360 \text{ cm}^3 \]

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