Calculate Cube Height from 25 cm² Base Area: Geometric Problem Solving

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

• Step 1: Identify the given information
• Step 2: Apply the appropriate formula
• Step 3: Perform the necessary calculations

Now, let's work through each step:
Step 1: The problem gives us the base area of the cube, which is 25 cm².
Step 2: We'll use the formula for the area of a square: $s^2 = 25$, where $s$ is the side length of the base, and also the height of the cube.
Step 3: Solve the equation $s^2 = 25$ by taking the square root of both sides to find $s$, the height of the cube.

Therefore, the height $s$ of the cube is $\sqrt{25} = 5$ cm.

Hence, the solution to the problem is $5$.