Calculate Cube Height from 36 cm² Base Area: Geometric Problem Solving

The cube shown below has a base area equal to 36 cm².

Is it possible to calculate the height of the cube? If so, what is it?

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

• Step 1: Understand the relationship between the base area and the side length of a cube.
• Step 2: Calculate the side length using the square area formula.
• Step 3: Conclude that the height of the cube is equal to this side length.

Now, let's work through each step:

Step 1: The basic property of a cube is that all of its three dimensions (length, width, and height) are equal. We know the base area of this cube is given as 36 cm².

Step 2: Using the formula for the area of a square, we have $s^2 = 36$, where $s$ is the side length of the base.

Solving for $s$, we find:

$s = \sqrt{36} = 6 \, \text{cm}$

Step 3: Since all sides of a cube are equal, the height of the cube is also $6 \, \text{cm}$.

Therefore, the height of the cube is $6 \, \text{cm}$.