Length of diagonal of a cube is `10sqrt3 cm`, find its volume.

Options

A. `100cm^3`
B. `600cm^3`
C. `1000 cm^3`
D. `10cm^3`

Answer

To find the volume of a cube when the length of its diagonal is given, 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: Substitute the given diagonal length into the formula.
We are given that the diagonal \( d \) is \( 10\sqrt{3} \) cm. Therefore, we can set up the equation:
\[ 10\sqrt{3} = a \sqrt{3} \]

### Step 3: Solve for the side length \( a \).
To find \( a \), we can divide both sides of the equation by \( \sqrt{3} \):
\[ a = 10 \text{ cm} \]

### Step 4: Calculate the volume of the cube.
The volume \( V \) of a cube is calculated using the formula:
\[ V = a^3 \]
Substituting the value of \( a \):
\[ V = 10^3 = 1000 \text{ cubic cm} \]

### Step 5: Conclusion.
Thus, the volume of the cube is \( 1000 \) cubic cm.

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