Calculating the volume of a square prism is a fundamental task in geometry and is often required in various practical applications. This article will guide you through the process of determining the volume using a specific algebraic formula. We will break down the formula, explain each component, and provide a step-by-step example calculation.
Volume of a Square Prism Formula
The volume (\( V \)) of a square prism can be calculated using the following formula:
\[ V = a^2 \cdot h \]
Where:
- \( a \) is the length of one side of the square base.
- \( h \) is the height (or depth) of the prism.
Explanation of the Formula
- The term \( a^2 \) represents the area of the square base of the prism.
- Multiplying the area of the base by the height (\( h \)) gives the total volume of the prism.
Step-by-Step Calculation
Let's go through an example to demonstrate how to use this formula to find the volume of a square prism.
Example: Calculating the Volume of a Square Prism
1. Identify the given values:
- Side length of the square base (\( a \)) = 6 units
- Height (\( h \)) = 12 units
2. Substitute the values into the volume formula:
\[ V = 6^2 \cdot 12 \]
3. Calculate the area of the square base:
\[ 6^2 = 36 \]
4. Substitute the area back into the formula:
\[ V = 36 \cdot 12 \]
5. Complete the multiplication:
\[ V = 432 \text{ cubic units} \]
Final Volume
The volume of the square prism with a side length of 6 units and a height of 12 units is 432 cubic units.
