Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Definition of 3D Solids: Unlike 2D shapes which are flat, 3D solids have three dimensions: length, breadth (width), and height. They occupy space and have volume. Imagine a flat drawing of a square (2D) versus a physical wooden block (3D).
Faces: A face is the flat or curved surface of a 3D shape. For example, a cube looks like it is made of flat squares joined together. These squares are its faces.
Edges: An edge is a line segment where two faces of a solid meet. Think of it as the 'border' or the 'rim' of a side. In a cuboid, like a matchbox, you can feel the straight lines where the sides meet; those are the edges.
Vertices (Corners): A vertex (plural: vertices) is a point where three or more edges meet. It is often called a 'corner'. If you touch the sharp corner of a dice, you are touching a vertex.
Cube and Cuboid: A cube is a solid with equal square faces, edges, and vertices. A cuboid is similar but its faces are rectangles. Visually, a cube looks like a dice, while a cuboid looks like a brick or a textbook.
Cylinder: A cylinder has flat circular faces at the top and bottom and curved surface wrapped around them. It has curved edges and vertices. It looks like a battery or a straight pipe.
Sphere: A sphere is a perfectly round 3D shape with only curved surface. It has no flat faces, no edges, and no vertices. It looks like a ball or a marble from every direction.
Cone: A cone has flat circular face at the bottom and curved surface that tapers to a single point at the top called the apex. It has curved edge and vertex. It looks like an ice-cream cone or a birthday party hat.
📐Formulae
Total Faces of a Cube or Cuboid =
Total Edges of a Cube or Cuboid =
Total Vertices of a Cube or Cuboid =
Faces of a Cylinder =
Vertices of a Cone = (The Apex)
Properties of a Sphere:
💡Examples
Problem 1:
Identify the 3D solid that has rectangular faces, edges, and vertices. Give one real-life example of this shape.
Solution:
- Look at the properties: rectangular faces indicate a prism-like structure.
- Since the faces are rectangles, the shape is a Cuboid.
- Verify edges: .
- Verify vertices: .
- Real-life example: A brick or a pencil box.
Explanation:
By checking the number of faces and their shape (rectangles), we can distinguish between a cube (square faces) and a cuboid (rectangular faces).
Problem 2:
Rohan has a solid that has flat faces and curved surface. How many edges does this solid have, and what is the name of the shape?
Solution:
- A solid with flat circular faces and curved surface is a Cylinder.
- The flat faces meet the curved surface at the top and bottom.
- Each meeting point forms a curved edge.
- Therefore, the number of edges is .
Explanation:
A cylinder is unique because it combines flat circular ends with a curved middle, resulting in exactly curved edges.