Step 1: Understanding the Question:
The topic for this problem is Mensuration, specifically 3D Geometry involving a Cube. A cube is a three-dimensional solid object bounded by six square faces, where all edges have the same length. The "volume" of a cube represents the total space occupied by the object. To solve this, we simply need to understand the relationship between the side length and the space contained within the cube's boundaries.
Step 2 : Key Formulas and approach:
1. Volume of a Cube: $V = s^3$ or $V = \text{side} \times \text{side} \times \text{side}$.
2. Side Length (s): Given as 6 cm.
The approach is a direct substitution of the side length into the volume formula and performing the cube calculation.
Step 3 : Detailed Explanation:
We are given that the side of the cube is $6 \text{ cm}$. In a cube, length = width = height = 6 cm.
The formula for volume is $V = \text{side}^3$. Substituting our value, we get $V = 6 \times 6 \times 6$.
First, we calculate the area of the base (side squared): $6 \times 6 = 36 \text{ cm}^2$.
Then, we multiply this base area by the height (the third side): $36 \times 6$.
To calculate $36 \times 6$: $30 \times 6 = 180$ and $6 \times 6 = 36$. Adding them, $180 + 36 = 216$.
The units for side length are in centimeters (cm), so the units for volume will be cubic centimeters ($\text{cm}^3$).
Therefore, the total space occupied by the cube is 216 cubic centimeters.
It is interesting to note that for a cube of side 6, the numerical value of its Volume ($6^3 = 216$) is exactly equal to the numerical value of its Total Surface Area ($6 \times 6^2 = 216$), though the units differ ($\text{cm}^3$ vs $\text{cm}^2$).
Step 4 : Final Answer:
The volume of the cube is 216 cm³, which matches option (D).