The volume of the metal of a cylindrical pipe is `748 cm^(3)`. The length of the pipe is 14 cm and its external radius is 9 cm. Its thickness is (Take `pi = (22)/(7)`)

Options

A. 1 cm
B. 5.2 cm
C. 2.3 cm
D. 3.7 cm

Answer

To find the thickness of the cylindrical pipe, we can follow these steps:

### Step 1: Understand the volume of the cylindrical pipe
The volume of the metal in the cylindrical pipe is given by the formula:
\[ \text{Volume} = \pi (R^2 - r^2) h \]
where:
- \( R \) is the external radius,
- \( r \) is the internal radius,
- \( h \) is the height (length) of the pipe.

### Step 2: Identify the known values
From the question, we have:
- Volume \( = 748 \, \text{cm}^3 \)
- External radius \( R = 9 \, \text{cm} \)
- Height \( h = 14 \, \text{cm} \)
- \( \pi = \frac{22}{7} \)

### Step 3: Substitute the known values into the volume formula
Substituting the known values into the volume formula:
\[ 748 = \frac{22}{7} \left(9^2 - r^2\right) \cdot 14 \]

### Step 4: Simplify the equation
First, calculate \( 9^2 \):
\[ 9^2 = 81 \]
Now substitute this back into the equation:
\[ 748 = \frac{22}{7} (81 - r^2) \cdot 14 \]
Next, simplify the right side:
\[ 748 = \frac{22 \cdot 14}{7} (81 - r^2) \]
Calculating \( \frac{22 \cdot 14}{7} \):
\[ \frac{22 \cdot 14}{7} = \frac{308}{7} = 44 \]
So now we have:
\[ 748 = 44 (81 - r^2) \]

### Step 5: Divide both sides by 44
\[ \frac{748}{44} = 81 - r^2 \]
Calculating \( \frac{748}{44} \):
\[ \frac{748}{44} = 17 \]
Thus, we have:
\[ 17 = 81 - r^2 \]

### Step 6: Rearrange to find \( r^2 \)
Rearranging gives:
\[ r^2 = 81 - 17 \]
\[ r^2 = 64 \]

### Step 7: Take the square root to find \( r \)
Taking the square root of both sides:
\[ r = \sqrt{64} = 8 \, \text{cm} \]

### Step 8: Calculate the thickness of the pipe
The thickness \( t \) of the pipe is the difference between the external radius and the internal radius:
\[ t = R - r = 9 \, \text{cm} - 8 \, \text{cm} = 1 \, \text{cm} \]

### Final Answer
The thickness of the cylindrical pipe is \( 1 \, \text{cm} \).

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