Determining the surface area of a cube is a straightforward process if you know the length of one of its sides. This article will guide you through the calculation using a simple algebraic formula.
Formula to Calculate the Surface Area of a Cube
The surface area \( SA \) of a cube can be calculated using the following formula:
\[ SA = 6 \cdot a^2 \]
Where:
- \( SA \) is the surface area of the cube.
- \( a \) is the length of one side of the cube.
Explanation of the Formula
A cube has six faces, each of which is a square. The area of one square face is \( a^2 \). Since the cube has six identical faces, the total surface area is six times the area of one face. Hence, the formula \( SA = 6 \cdot a^2 \).
Example Calculation
Let's go through an example to illustrate how to use this formula.
Given:
- \( a = 4 \) units (the length of one side of the cube)
We want to find the surface area of the cube.
Step 1: Identify the Given Value
Given:
- \( a = 4 \) units
Step 2: Use the Surface Area Formula
\[ SA = 6 \cdot a^2 \]
Step 3: Substitute the Given Value into the Formula
\[ SA = 6 \cdot (4^2) \]
Step 4: Calculate the Value
\[ 4^2 = 16 \]
\[ SA = 6 \cdot 16 \]
\[ SA = 96 \]
Final Value
The surface area of a cube with a side length of 4 units is 96 square units.
By following these steps, you can easily calculate the surface area of a cube when you know the length of one of its sides. This straightforward method involves squaring the side length and multiplying by six to get the total surface area.
