The length of diagonal of a cube is `( 14sqrt 3)` The volume of the cube is -------

Options

A. `256 cm^3`
B. `2744cm^3`
C. `588 cm^3`
D. `3528 cm^3`

Answer

To find the volume of the cube given the length of its diagonal, we can follow these steps:

### Step 1: Understand the relationship between the diagonal and the side length of the cube.
The formula for the diagonal \( d \) of a cube in terms of its side length \( a \) is given by:
\[ d = a \sqrt{3} \]

### Step 2: Substitute the given diagonal length into the formula.
We know the length of the diagonal is \( 14\sqrt{3} \). Therefore, we can set up the equation:
\[ 14\sqrt{3} = a\sqrt{3} \]

### Step 3: Solve for the side length \( a \).
To isolate \( a \), we can divide both sides of the equation by \( \sqrt{3} \):
\[ a = 14 \]

### Step 4: Calculate the volume of the cube.
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
Substituting the value of \( a \):
\[ V = 14^3 \]

### Step 5: Calculate \( 14^3 \).
Now, we calculate \( 14^3 \):
\[ 14^3 = 14 \times 14 \times 14 = 196 \times 14 = 2744 \]

### Conclusion:
The volume of the cube is \( 2744 \, \text{cm}^3 \).

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