The volume of a cuboid is ` 7. 68 m ^(3) ` if its length = 3.2 m and height = 1.0 m find its breadth.

Answer

To find the breadth of the cuboid, we will use the formula for the volume of a cuboid, which is given by:

\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]

### Step-by-step Solution:

1. **Identify the given values:**
- Volume \( V = 7.68 \, m^3 \)
- Length \( L = 3.2 \, m \)
- Height \( H = 1.0 \, m \)
- Let the breadth be \( B \).

2. **Write the formula for the volume of a cuboid:**
\[ V = L \times B \times H \]

3. **Substitute the known values into the formula:**
\[ 7.68 = 3.2 \times B \times 1.0 \]

4. **Simplify the equation:**
\[ 7.68 = 3.2 \times B \]

5. **Solve for breadth \( B \):**
\[ B = \frac{7.68}{3.2} \]

6. **Perform the division:**
- To simplify \( \frac{7.68}{3.2} \), we can remove the decimal by multiplying both the numerator and the denominator by 10:
\[ B = \frac{76.8}{32} \]

7. **Calculate \( B \):**
- Now, divide \( 76.8 \) by \( 32 \):
\[ 32 \times 2 = 64 \quad (\text{which is less than } 76.8) \]
\[ 32 \times 3 = 96 \quad (\text{which is greater than } 76.8) \]
- Therefore, we can try \( 32 \times 2.4 = 76.8 \).
- Thus, \( B = 2.4 \, m \).

### Final Answer:
The breadth of the cuboid is \( 2.4 \, m \).

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