The volume of a metallic cylindrical pipe is `1232 cm^3`. If its external radius is 7 cm and thickness is 2 cm, then the length of the pipe (correct to one decimal place) (in cm) is: (Take `pi = 22/7`)

Options

A. 18.5
B. 17.2
C. 15.7
D. 14.2

Answer

To find the length of the metallic cylindrical pipe, we can use the formula for the volume of a hollow cylinder, which is given by:

\[ V = \pi h (R^2 - r^2) \]

where:
- \( V \) is the volume of the pipe,
- \( h \) is the height (or length) of the pipe,
- \( R \) is the external radius,
- \( r \) is the internal radius.

### Step 1: Identify the values
From the problem statement:
- Volume \( V = 1232 \, \text{cm}^3 \)
- External radius \( R = 7 \, \text{cm} \)
- Thickness of the pipe \( t = 2 \, \text{cm} \)

### Step 2: Calculate the internal radius
The internal radius \( r \) can be calculated as:
\[ r = R - t = 7 \, \text{cm} - 2 \, \text{cm} = 5 \, \text{cm} \]

### Step 3: Substitute the values into the volume formula
Now, substitute \( V \), \( R \), and \( r \) into the volume formula:
\[ 1232 = \frac{22}{7} h (7^2 - 5^2) \]

### Step 4: Calculate \( R^2 - r^2 \)
Calculate \( R^2 \) and \( r^2 \):
\[ R^2 = 7^2 = 49 \]
\[ r^2 = 5^2 = 25 \]
\[ R^2 - r^2 = 49 - 25 = 24 \]

### Step 5: Substitute back into the equation
Now substitute \( R^2 - r^2 \) back into the equation:
\[ 1232 = \frac{22}{7} h (24) \]

### Step 6: Simplify the equation
Multiply both sides by \( \frac{7}{22} \):
\[ h = \frac{1232 \times 7}{22 \times 24} \]

### Step 7: Calculate \( h \)
Now calculate the right-hand side:
\[ h = \frac{1232 \times 7}{528} \]
\[ h = \frac{8624}{528} \]

### Step 8: Simplify the fraction
Now simplify \( \frac{8624}{528} \):
\[ h = 16.3333 \ldots \text{ cm} \]

### Step 9: Round to one decimal place
Finally, round \( h \) to one decimal place:
\[ h \approx 16.3 \, \text{cm} \]

### Final Answer
The length of the pipe is approximately \( 16.3 \, \text{cm} \).

---