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What is the Hexahedron (Cube)?
Grade Level:
Class 7
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
A hexahedron is a 3D shape with six flat faces. The most common type of hexahedron is a cube, where all six faces are identical squares. Think of it as a perfect box.
Simple Example
Quick Example
Imagine you have a Rubik's Cube. It has six perfectly square sides, and each side is a face. That Rubik's Cube is a perfect example of a hexahedron, specifically a cube.
Worked Example
Step-by-Step
Let's find the total number of faces, edges, and vertices for a cube. --- Step 1: Count the faces. A cube has a top, bottom, front, back, left, and right face. So, there are 6 faces. --- Step 2: Count the edges. Edges are where two faces meet. Count the lines: 4 on the top, 4 on the bottom, and 4 connecting the top to the bottom. So, there are 12 edges. --- Step 3: Count the vertices. Vertices are the corners where edges meet. There are 4 corners on the top face and 4 corners on the bottom face. So, there are 8 vertices. --- Answer: A cube has 6 faces, 12 edges, and 8 vertices.
Why It Matters
Common Mistakes
MISTAKE: Confusing a cube with a cuboid. | CORRECTION: A cube has all square faces of equal size, while a cuboid can have rectangular faces of different sizes (like a brick). All cubes are cuboids, but not all cuboids are cubes.
MISTAKE: Miscounting the number of edges or vertices. | CORRECTION: Always count systematically. For edges, count the top, bottom, then vertical connecting edges. For vertices, count the corners on the top face then the bottom face.
MISTAKE: Thinking a hexahedron is only a cube. | CORRECTION: A cube is a *type* of hexahedron. A hexahedron simply means 'six faces.' There are other hexahedrons that are not cubes, like a rectangular prism (cuboid).
Practice Questions
Try It Yourself
QUESTION: How many faces does a standard dice (ludo dice) have? | ANSWER: 6 faces
QUESTION: If you stack two identical cubes on top of each other, how many total faces would the new solid have? (Think carefully about the faces that touch) | ANSWER: The top cube has 5 exposed faces (top, 4 sides). The bottom cube has 5 exposed faces (bottom, 4 sides). So, 5 + 5 = 10 exposed faces.
QUESTION: A small gift box is shaped like a cube. If each edge of the box is 5 cm long, what is the total length of all its edges combined? | ANSWER: A cube has 12 edges. Each edge is 5 cm. So, 12 * 5 cm = 60 cm.
MCQ
Quick Quiz
Which of these objects is an example of a cube?
A cricket ball
A water bottle
A Rubik's Cube
A pizza slice
The Correct Answer Is:
C
A Rubik's Cube has six identical square faces, making it a perfect example of a cube. The other options are different shapes.
Real World Connection
In the Real World
Cubes are everywhere! Your ice cubes in a glass of nimbu pani, the dice you play Ludo with, or even some small storage boxes are all examples of cubes. In architecture, designers might use cube-like modules for building structures, and in gaming, many simple 3D characters or blocks are built using cube shapes.
Key Vocabulary
Key Terms
FACE: A flat surface of a 3D shape | EDGE: The line segment where two faces meet | VERTEX: A corner point where edges meet | 3D SHAPE: A shape that has length, width, and height
What's Next
What to Learn Next
Great job understanding the cube! Next, you can explore other 3D shapes like cuboids, pyramids, and prisms. You'll learn how they are different from cubes and how to calculate their surface area and volume, which is super useful!
