If diagonal of a cube is `sqrt(12) cm`, then its volume in cubic cm is :

Options

A. 8
B. 12
C. 24
D. `3sqrt(2)`

Answer

To find the volume of the cube given that the diagonal is \( \sqrt{12} \) cm, we can follow these steps:

### Step 1: Understand the relationship between the diagonal and the side 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: Set up the equation with the given diagonal.
We know that the diagonal \( d \) is \( \sqrt{12} \) cm. Therefore, we can set up the equation:
\[ a \sqrt{3} = \sqrt{12} \]

### Step 3: Simplify \( \sqrt{12} \).
We can simplify \( \sqrt{12} \):
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
Now we can rewrite our equation:
\[ a \sqrt{3} = 2\sqrt{3} \]

### Step 4: Solve for \( a \).
To find \( a \), we can divide both sides of the equation by \( \sqrt{3} \):
\[ a = \frac{2\sqrt{3}}{\sqrt{3}} = 2 \]

### Step 5: Calculate the volume of the cube.
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
Substituting the value of \( a \):
\[ V = 2^3 = 8 \text{ cm}^3 \]

### Final Answer:
The volume of the cube is \( 8 \text{ cm}^3 \).

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