The volume of a wall , 3 times as high as it is broad and 8 times as long as it is high, is ` 36.864 m^(3)`. The height of the wall is :

Options

A. 1.8 m
B. 2.4 m
C. 4.2 m
D. none of these

Answer

To find the height of the wall, we will follow these steps:

### Step 1: Define the variables
Let the height of the wall be \( x \) meters.

### Step 2: Express the dimensions in terms of \( x \)
According to the problem:
- The breadth of the wall is \( 3 \) times the height, so the breadth is \( 3x \).
- The length of the wall is \( 8 \) times the height, so the length is \( 8x \).

### Step 3: Write the formula for the volume of the wall
The volume \( V \) of a cuboid is given by the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Substituting the expressions for length, breadth, and height:
\[ V = (8x) \times (3x) \times x \]

### Step 4: Simplify the volume expression
\[ V = 24x^3 \]

### Step 5: Set the volume equal to the given volume
The problem states that the volume of the wall is \( 36.864 \, m^3 \):
\[ 24x^3 = 36.864 \]

### Step 6: Solve for \( x^3 \)
To isolate \( x^3 \), divide both sides by \( 24 \):
\[ x^3 = \frac{36.864}{24} \]
Calculating the right side:
\[ x^3 = 1.536 \]

### Step 7: Calculate \( x \)
To find \( x \), take the cube root of both sides:
\[ x = \sqrt[3]{1.536} \]
Calculating the cube root:
\[ x \approx 1.1447 \, m \]

### Step 8: Conclusion
Thus, the height of the wall is approximately \( 1.1447 \, m \).