Mathematics
Grade 10
15 min
Three-dimensional figure vocabulary
Three-dimensional figure vocabulary
What you'll learn
- Draw a model to represent the multiplication of a unit fraction by a whole number with 80% accuracy.
- Solve multiplication problems involving unit fractions and whole numbers, showing your work using models, with at least 70% accuracy on a worksheet.
- Explain how a model represents the multiplication of a unit fraction by a whole number in your own words, demonstrating understanding in a short written response.
- Identify the product of a unit fraction multiplied by a whole number from a set of 4 possible answers with 85% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define key vocabulary terms such as polyhedron, face, edge, and vertex.
Identify the faces, edges, and vertices on a given three-dimensional figure.
Differentiate between prisms and pyramids based on their defining characteristics.
Classify polyhedra by the shape of their base (e.g., triangular prism, square pyramid).
Apply Euler's formula to verify the relationship between the faces, vertices, and edges of a convex polyhedron.
Distinguish between right and oblique solids.
Ever wonder how architects design skyscrapers or how game developers create realistic 3D worlds? 🏙️ It all starts with a shared language for describing shapes!
This tutorial introduces the fundamental vocabulary used to describe three-dimensional figures. Mastering these terms is...
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Key Concepts & Vocabulary
TermDefinitionExample
PolyhedronA three-dimensional solid figure whose surfaces are flat polygons. It has no curved surfaces.A cube, a pyramid, or a soccer ball (which is a truncated icosahedron).
FaceOne of the flat polygonal surfaces of a polyhedron.A cube has 6 square faces.
EdgeA line segment formed by the intersection of two faces of a polyhedron.A cube has 12 edges.
Vertex (plural: Vertices)A point where three or more edges meet; a corner of a polyhedron.A cube has 8 vertices.
PrismA polyhedron with two parallel, congruent polygonal bases and lateral faces that are parallelograms (typically rectangles in a right prism).A Toblerone box is a triangular prism.
PyramidA polyhedron with one polygonal base and triangular lateral faces that meet at a single common vertex called the apex.Th...
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Core Formulas
Euler's Formula for Polyhedra
V - E + F = 2
For any convex polyhedron, the number of Vertices (V) minus the number of Edges (E) plus the number of Faces (F) always equals 2. This is a powerful tool for verifying your counts of a figure's parts.
Naming Prisms and Pyramids
Name = (Base Shape) + (Solid Type)
The name of a prism or pyramid is determined by the shape of its base. For example, a prism with a pentagonal base is a 'pentagonal prism', and a pyramid with a hexagonal base is a 'hexagonal pyramid'.
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Challenging
If a prism has an n-sided polygon (n-gon) as its base, which expression correctly represents the total number of its faces (F)?
A.F = 2n
B.F = n + 1
C.F = n + 2
D.F = 3n
Challenging
Two identical square pyramids are joined at their square bases, forming a new convex polyhedron (an octahedron). What are the number of vertices (V), edges (E), and faces (F) for this new solid?
A.V=6, E=12, F=8
B.V=8, E=12, F=6
C.V=5, E=8, F=5
D.V=10, E=16, F=8
Challenging
An artist creates a right pentagonal prism. They then deform it into an oblique pentagonal prism by slanting the lateral edges, without breaking any connections. Which statement is true about the oblique prism compared to the original right prism?
A.The number of edges has increased.
B.The value of V - E + F has changed.
C.The shape of the lateral faces is no longer a parallelogram.
D.The number of faces, edges, and vertices remains the same.
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Frequently asked questions
What grade level is "Three-dimensional figure vocabulary"?
Three-dimensional figure vocabulary is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Three-dimensional figure vocabulary?
You'll be able to: Draw a model to represent the multiplication of a unit fraction by a whole number with 80% accuracy; Solve multiplication problems involving unit fractions and whole numbers, showing your work using models, with at least 70%….
Is "Three-dimensional figure vocabulary" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Three-dimensional figure vocabulary?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.