A hollow square shaped tube open at both ends is made of iron. The internal square is of 5 cm side and the length of the tube is 8 cm . There are `192 cm^(3) ` of iron in the tube . Find its thickness :

Options

A. 2 cm
B. 0.5 cm
C. 1 cm
D. can't be determined

Answer

To find the thickness of the hollow square-shaped tube, we will follow these steps:

### Step 1: Understand the dimensions of the tube
- The internal square has a side length of 5 cm.
- The length of the tube is 8 cm.
- The volume of iron used in the tube is 192 cm³.

### Step 2: Set up the equation for the volume of the iron
Let the side length of the outer square be \( x \) cm. The area of the outer square is \( x^2 \) and the area of the inner square is \( 5^2 = 25 \) cm².

The volume of the iron in the tube can be expressed as:
\[ \text{Volume of iron} = (\text{Area of outer square} - \text{Area of inner square}) \times \text{Length} \]
Substituting the known values:
\[ 192 = (x^2 - 25) \times 8 \]

### Step 3: Solve for \( x^2 \)
First, simplify the equation:
\[ 192 = 8(x^2 - 25) \]
Dividing both sides by 8:
\[ 24 = x^2 - 25 \]
Now, add 25 to both sides:
\[ x^2 = 24 + 25 \]
\[ x^2 = 49 \]

### Step 4: Find \( x \)
Taking the square root of both sides:
\[ x = \sqrt{49} = 7 \text{ cm} \]

### Step 5: Calculate the thickness of the tube
The thickness of the tube is the difference between the outer and inner square sides divided by 2:
\[ \text{Thickness} = \frac{x - 5}{2} = \frac{7 - 5}{2} = \frac{2}{2} = 1 \text{ cm} \]

### Final Answer
The thickness of the tube is **1 cm**.

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