A cube has numerically equal volume and surface area. The volume of such a cube is

Options

A. 216 unit
B. 300 unit
C. 636 unit
D. 1000 unit

Explanation

To solve the problem of finding the volume of a cube that has numerically equal volume and surface area, we can follow these steps:

### Step-by-Step Solution

1. **Understand the Formulas**:
- The volume \( V \) of a cube with side length \( a \) is given by:
\[ V = a^3 \]
- The surface area \( S \) of a cube is given by:
\[ S = 6a^2 \]

2. **Set Up the Equation**:
- According to the problem, the volume is equal to the surface area:
\[ a^3 = 6a^2 \]

3. **Simplify the Equation**:
- We can simplify the equation by dividing both sides by \( a^2 \) (assuming \( a \neq 0 \)):
\[ a = 6 \]

4. **Calculate the Volume**:
- Now that we have the side length \( a \), we can find the volume:
\[ V = a^3 = 6^3 = 216 \]

5. **Conclusion**:
- Therefore, the volume of the cube is:
\[ V = 216 \text{ cubic units} \]

### Final Answer
The volume of the cube is **216 cubic units**.