Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
3D shapes (solids) have three dimensions: length, width, and height.
Faces: The flat or curved surfaces that make up the outside of a 3D shape.
Edges: The lines where two faces meet.
Vertices: The corner points where three or more edges meet (singular: vertex).
Prisms: 3D shapes with two identical ends (bases) and flat sides. They have the same cross-section all along their length.
Pyramids: 3D shapes with a polygon base and triangular faces that meet at a single point (apex).
Nets: A 2D flat pattern that can be folded to create a 3D shape.
Identifying Nets: Every face in the 3D shape must be represented in the net, and they must be positioned so they don't overlap when folded.
📐Formulae
Euler's Formula for Polyhedra: (where = Faces, = Vertices, = Edges)
Cube Properties:
Square-based Pyramid Properties:
Triangular Prism Properties:
💡Examples
Problem 1:
Identify the 3D shape that consists of 2 circular faces and 1 curved surface. What would its net look like?
Solution:
Cylinder.
Explanation:
A cylinder has two identical circular bases at the top and bottom. Its net consists of two circles and one rectangle (which wraps around to form the curved surface).
Problem 2:
A 3D shape has 4 triangular faces and 4 vertices. Name the shape and describe its net.
Solution:
Triangular-based pyramid (or Tetrahedron).
Explanation:
Since all 4 faces are triangles, it is a tetrahedron. Its net consists of four triangles joined together; commonly seen as one central triangle with three other triangles attached to its sides.
Problem 3:
If a shape is a hexagonal prism, how many faces, vertices, and edges does it have?
Solution:
Faces: 8, Vertices: 12, Edges: 18.
Explanation:
A hexagonal prism has 2 hexagonal bases and 6 rectangular side faces (). It has 6 vertices on the top base and 6 on the bottom (). It has 6 edges on the top, 6 on the bottom, and 6 vertical edges connecting them ().
Problem 4:
Which 3D shape has a net made of one square and four triangles?
Solution:
Square-based pyramid.
Explanation:
The square acts as the base of the pyramid, and the four triangles fold up to meet at a single point (vertex) above the center of the square.