A wall is 5 times as high as it is broad and 8 times as long as it is high. If the volume of the wall is 12.8 `m^3` then find the breadth of the wall.

Options

A. 30 cm
B. 40 cm
C. 22.5 cm
D. 25 cm

Answer

To solve the problem step by step, we will define the dimensions of the wall based on the information provided and use the formula for volume to find the breadth.

### Step-by-Step Solution:

1. **Define the Variables:**
Let the breadth of the wall be \( x \) meters.

2. **Determine the Height:**
According to the problem, the height of the wall is 5 times the breadth. Therefore, the height \( h \) can be expressed as:
\[ h = 5x \]

3. **Determine the Length:**
The problem states that the length of the wall is 8 times the height. Thus, the length \( l \) can be expressed as:
\[ l = 8h = 8(5x) = 40x \]

4. **Volume of the Wall:**
The volume \( V \) of the wall is given by the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Substituting the expressions for length, breadth, and height, we get:
\[ V = l \times x \times h = (40x) \times x \times (5x) = 200x^3 \]

5. **Set Up the Equation:**
We know the volume of the wall is 12.8 m³. Therefore, we can set up the equation:
\[ 200x^3 = 12.8 \]

6. **Solve for \( x^3 \):**
To find \( x^3 \), we divide both sides of the equation by 200:
\[ x^3 = \frac{12.8}{200} = 0.064 \]

7. **Find \( x \):**
To find \( x \), we take the cube root of both sides:
\[ x = \sqrt[3]{0.064} = 0.4 \text{ meters} \]

8. **Convert to Centimeters:**
Since the question may require the answer in centimeters, we convert meters to centimeters:
\[ x = 0.4 \text{ m} = 40 \text{ cm} \]

### Final Answer:
The breadth of the wall is \( 40 \text{ cm} \).