The side of solid metallic cube is 20 cm. The cube is melted and recast into 8 equal solid cubical dice. Determine the side of the dice.

Options

A. 7 cm
B. 9 cm
C. 8 cm
D. 10 cm

Answer

To find the side of the small cubical dice formed from the solid metallic cube, we can follow these steps:

### Step-by-Step Solution:

1. **Find the Volume of the Original Cube**:
The side of the original cube is given as 20 cm. The volume \( V \) of a cube is calculated using the formula:
\[ V = \text{side}^3 \]
Therefore, the volume of the original cube is:
\[ V = 20^3 = 20 \times 20 \times 20 = 8000 \, \text{cm}^3 \]

2. **Determine the Volume of Each Dice**:
The original cube is melted and recast into 8 equal solid cubical dice. Let the side of each die be \( x \). The volume of one die is given by:
\[ \text{Volume of one die} = x^3 \]
Since there are 8 dice, the total volume of the 8 dice is:
\[ \text{Total volume of 8 dice} = 8 \times x^3 \]

3. **Set the Volumes Equal**:
The volume of the original cube is equal to the total volume of the 8 dice:
\[ 8000 = 8x^3 \]

4. **Solve for \( x^3 \)**:
To find \( x^3 \), divide both sides of the equation by 8:
\[ x^3 = \frac{8000}{8} = 1000 \]

5. **Find the Side Length \( x \)**:
To find \( x \), take the cube root of both sides:
\[ x = \sqrt[3]{1000} \]
Since \( 1000 = 10^3 \), we have:
\[ x = 10 \, \text{cm} \]

### Final Answer:
The side of each cubical die is \( 10 \, \text{cm} \).

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