This article examines the relationship between volume and surface area of a cube, specifically considering a cube with a volume of 125 cm³. By deriving the formula for calculating the surface area of a cube and applying it to this specific case, we aim to determine the exact value of the surface area.
Additionally, this study explores various geometric properties inherent in cubes, providing insight into their structural characteristics.
The objective and impersonal nature of this academic writing style ensures an unbiased analysis of these mathematical concepts.
The Volume Of A Cube Is 125 Cm³. What Is The Surface Area Of The Cube?
To find the surface area of a cube when its volume is 125 cm³, you first need to calculate the side length of the cube. Since a cube has all sides of equal length (s), and the volume of a cube is V = s³, you can find that s = ∛(125 cm³) = 5 cm. Then, the surface area is 6s², which equals 6 * (5 cm)² = 150 cm².
| Step | Calculation | Result |
|---|---|---|
| Find the side length (s) | s = ∛(Volume) = ∛(125 cm³) = 5 cm | 5 cm |
| Calculate the surface area | Surface Area = 6s² | 6 * (5 cm)² = 150 cm² |
Key Takeaways
- The volume of a cube can be calculated using the formula V = s^3, where V represents volume and s represents the length of the side of the cube.
- The surface area of a cube can be calculated using the formula SA = 6s^2, where SA represents surface area and s represents the length of the side of the cube.
- As the volume of a cube increases, the surface area also increases.
- Understanding the relationship between volume and surface area is important for practical applications such as material estimation, space optimization, and architectural and engineering calculations.
Understanding the Relationship between Volume and Surface Area
The relationship between the volume and surface area of a cube is an important concept in geometry. In a cube, all sides are equal in length, which makes it a regular polyhedron.
The formula to calculate the volume of a cube is V = s^3, where s represents the length of each side. On the other hand, the formula to calculate the surface area is SA = 6s^2.
This relationship shows that as the volume of a cube increases, so does its surface area. Understanding this relationship allows for practical applications such as determining how much material is needed to construct a cube-shaped container or calculating the amount of paint required to cover its surfaces.
It also aids in optimizing space utilization and geometric design in various fields such as architecture and engineering.
Deriving the Formula for Surface Area of a Cube
with triangular faces.
Applying the Formula to Find the Surface Area
Applying the formula for calculating the surface area of a cube involves multiplying the side length by itself and then multiplying that result by 6.
This formula can be applied in various real-life situations to determine the total exposed area of a cube-shaped object.
For example, architects and engineers can use this formula to calculate the surface area of a building’s exterior walls, allowing them to accurately estimate material requirements or evaluate heat transfer rates.
Additionally, manufacturers can utilize this formula to determine the amount of paint or coating needed to cover a cube-shaped product.
The advantages of using the surface area formula include its simplicity and efficiency in obtaining accurate measurements in three-dimensional objects with parallel faces.
Exploring the Geometric Properties of Cubes
Exploring the geometric properties of cubes involves examining the equal length of their edges and the presence of parallel faces. Cubes are three-dimensional objects that possess several interesting characteristics. Some key aspects to consider when exploring the geometric properties of cubes include:
- Equal Edge Length: All edges of a cube have the same length, making it a regular polyhedron.
- Parallel Faces: A cube has six square faces that are all parallel to each other.
- Symmetry: A cube possesses multiple axes of symmetry, allowing for various orientations and arrangements.
Furthermore, studying the applications of cubes in architecture and design reveals their versatility in creating functional and aesthetically pleasing structures. Additionally, investigating the connection between cubes and other three-dimensional shapes can provide insights into how different shapes relate to one another within mathematical systems.
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