The volume (in my) of a cube whose diagonal is 2.5 metre, is :

Options

A. `(125sqrt(3))/(72)`
B. `625/8`
C. `(125sqrt(2))/(32)`
D. `(125)/8`

Answer

To find the volume of a cube whose diagonal is given as 2.5 meters, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between the side and the diagonal of a cube**:
The diagonal \(d\) of a cube is related to its side length \(a\) by the formula:
\[ d = a \sqrt{3} \]

2. **Substitute the given diagonal into the formula**:
We know the diagonal \(d = 2.5\) meters, so we can set up the equation:
\[ 2.5 = a \sqrt{3} \]

3. **Solve for the side length \(a\)**:
To find \(a\), we rearrange the equation:
\[ a = \frac{2.5}{\sqrt{3}} \]

4. **Calculate \(a\)**:
To simplify \(a\), we can multiply the numerator and denominator by \(\sqrt{3}\):
\[ a = \frac{2.5 \sqrt{3}}{3} \]

5. **Find the volume of the cube**:
The volume \(V\) of a cube is given by:
\[ V = a^3 \]
Substituting \(a\) into the volume formula:
\[ V = \left(\frac{2.5 \sqrt{3}}{3}\right)^3 \]

6. **Calculate \(V\)**:
Expanding the volume:
\[ V = \frac{(2.5)^3 (\sqrt{3})^3}{3^3} \]
\[ V = \frac{15.625 \cdot 3\sqrt{3}}{27} \]
\[ V = \frac{46.875 \sqrt{3}}{27} \]

7. **Final simplification**:
We can simplify the fraction:
\[ V = \frac{125}{72} \sqrt{3} \text{ cubic meters} \]

### Final Answer:
The volume of the cube is:
\[ \frac{125 \sqrt{3}}{72} \text{ cubic meters} \]