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 Problem
We are given the volume of the metal of a cylindrical pipe, the length of the pipe, and the external radius. We need to find the thickness of the pipe.

### Step 2: Use the Volume Formula for a Hollow Cylinder
The volume \( V \) of a hollow cylinder (the metal part) can be calculated using the formula:
\[ V = \pi (R^2 - r^2) h \]
where:
- \( R \) = external radius
- \( r \) = internal radius
- \( h \) = height (or length) of the cylinder

### Step 3: Substitute the Known Values
We know:
- \( V = 748 \, \text{cm}^3 \)
- \( R = 9 \, \text{cm} \)
- \( h = 14 \, \text{cm} \)
- \( \pi = \frac{22}{7} \)

Substituting these values into the volume formula:
\[ 748 = \frac{22}{7} (9^2 - r^2) \times 14 \]

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

### Step 5: Solve for \( r^2 \)
Now divide both sides by 44:
\[ \frac{748}{44} = 81 - r^2 \]
Calculating \( \frac{748}{44} \):
\[ \frac{748}{44} = 17 \]
Thus, we have:
\[ 17 = 81 - r^2 \]
Rearranging gives:
\[ r^2 = 81 - 17 = 64 \]

### Step 6: Find \( r \)
Taking the square root of both sides:
\[ r = \sqrt{64} = 8 \, \text{cm} \]

### Step 7: Calculate the Thickness
The thickness \( t \) of the pipe is given by:
\[ t = R - r \]
Substituting the values:
\[ t = 9 \, \text{cm} - 8 \, \text{cm} = 1 \, \text{cm} \]

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

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