Review the key concepts, formulae, and examples before starting your quiz.
đConcepts
3D shapes are solid objects that have three dimensions: length, width, and height.
Faces: The flat or curved surfaces that make up the outside of a 3D shape.
Edges: The straight or curved lines where two faces meet.
Vertices: The corners or points where two or more edges meet (singular: vertex).
Prisms: Shapes with two identical ends (bases) and the same cross-section all along their length (e.g., triangular prism, cube, cuboid).
Pyramids: Shapes with a flat base (like a square or triangle) and triangular sides that meet at a single point at the top called the apex.
Spheres: Perfectly round 3D shapes, like a ball, with one continuous curved surface and no edges or vertices.
đFormulae
(Euler's Formula for polyhedra)
đĄExamples
Problem 1:
Identify the 3D shape that has 1 square base and 4 triangular faces that meet at a point.
Solution:
Square-based Pyramid
Explanation:
A pyramid is named after its base. Since the base is a square and the sides are triangles meeting at an apex, it is a square-based pyramid.
Problem 2:
How many faces, edges, and vertices does a triangular prism have?
Solution:
5 faces, 9 edges, and 6 vertices.
Explanation:
A triangular prism has 2 triangular faces (the ends) and 3 rectangular faces. It has 3 edges around each triangle plus 3 connecting edges (). It has 3 vertices on each triangular face ().
Problem 3:
Which 3D shape has no flat faces, no edges, and no vertices?
Solution:
Sphere
Explanation:
A sphere is a perfectly round solid. Because it is completely curved, it does not have any flat surfaces (faces), sharp lines (edges), or corners (vertices).