Calculating Surface Area and Volume of a Cube
A cube is a three-dimensional geometric shape with six equal square faces. To calculate both the surface area and volume, we can use specific formulas based on the length of the edges.
Step 1: Calculate Surface Area
The formula for the surface area (SA) of a cube is given by:
SA = 6 * a²
Where a is the length of one edge of the cube. For our case:
- Edge length (a) = 4 cm
- SA = 6 * (4 cm)²
- SA = 6 * 16 cm²
- SA = 96 cm²
Thus, the surface area of the cube is 96 square centimeters.
Step 2: Calculate Volume
The formula for the volume (V) of a cube is:
V = a³
Using the same edge length:
- Edge length (a) = 4 cm
- V = (4 cm)³
- V = 64 cm³
Therefore, the volume of the cube is 64 cubic centimeters.
Conclusion
In summary, for a cube with an edge length of 4 cm:
- Surface Area: 96 cm²
- Volume: 64 cm³
These calculations illustrate how simple geometric properties can yield essential information about three-dimensional shapes.