Calculate Cube Height from 16 cm² Base Area: Geometric Problem Solving

To solve this problem, we'll follow these steps:

• Step 1: Identify the base area of the cube.
• Step 2: Use the formula to find the side length of the base.
• Step 3: Recognize that the height of the cube is equal to the side length of the base.

Now, let's work through each step:
Step 1: We are given the base area of the cube as $16 \, \text{cm}^2$.
Step 2: The area of a square is calculated using the formula $\text{side}^2$, where "side" is the length of each side of the square.
Setting up the equation: $\text{side}^2 = 16$. Solving for the "side," we find $\text{side} = \sqrt{16} = 4 \, \text{cm}$.
Step 3: Since the cube is a regular geometric shape, the height is equal to the side length of the base. Therefore, the height of the cube is $4 \, \text{cm}$.

Therefore, the height of the cube is $4 \, \text{cm}$.