Calculate Square Base Dimensions: 36 cm³ Rectangular Prism with Height 9

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

• Step 1: Write out the volume formula $V = x^2 \times h$, where $x$ is the side of the square base and $h$ is the height.
• Step 2: Substitute the given values $V = 36 \, \text{cm}^3$ and $h = 9 \, \text{cm}$ into the formula.
• Step 3: Solve for $x$.

Now, let's work through each step:
Step 1: The volume formula for the prism is $V = x^2 \times h$.
Step 2: Substitute the known values: $36 = x^2 \times 9$.
Step 3: Solve for $x$ by dividing both sides by 9: $x^2 = \frac{36}{9} = 4$.
To find $x$, take the square root of both sides: $x = \sqrt{4} = 2$.

Therefore, the length of each side of the square base is $x = 2 \, \text{cm}$.