Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
3D shapes 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 (singular: Vertex): The corners where three or more edges meet.
Prisms: Shapes with two identical ends (bases) and flat sides (e.g., cubes, cuboids, triangular prisms).
Pyramids: Shapes with a base and triangular faces that meet at a single point (apex).
Nets: A 2D pattern that can be folded to create a 3D shape. Each face in the net corresponds to a face on the 3D shape.
📐Formulae
Euler's Formula (for shapes with flat faces):
Number of faces on a prism =
Number of faces on a pyramid =
💡Examples
Problem 1:
Identify the 3D shape that has 6 square faces, 12 edges, and 8 vertices. Draw its net.
Solution:
The shape is a Cube.
Explanation:
A cube is a special type of cuboid where all faces are equal squares. Its net consists of 6 squares arranged in a 'cross' or 'T' shape that can fold to join all edges.
Problem 2:
A shape has one circular base and one curved surface that meets at a point (apex). Name the shape and describe its net.
Solution:
The shape is a Cone.
Explanation:
A cone consists of a circle (the base) and a sector of a circle (the curved part). When the sector is wrapped around the circle, it forms the cone's point.
Problem 3:
Which 3D shape is formed by a net consisting of two identical triangles and three rectangles?
Solution:
Triangular Prism.
Explanation:
Prisms are named after their base. Since there are two triangles, these are the bases. The three rectangles connect the three sides of the triangles, forming a triangular prism.
Problem 4:
Count the faces, edges, and vertices of a Square-based Pyramid.
Solution:
Faces: 5, Edges: 8, Vertices: 5.
Explanation:
A square-based pyramid has 1 square base and 4 triangular faces (Total 5 faces). It has 4 edges around the base and 4 edges leading to the top (Total 8 edges). It has 4 corners at the base and 1 at the top (Total 5 vertices).