Mathematics
Grade 10
15 min
Parts of three-dimensional figures (Review)
Parts of three-dimensional figures (Review)
What you'll learn
- Draw a number line and divide it into equal parts to represent a unit fraction.
- Show repeated addition of a unit fraction on a number line to visually represent multiplying it by a whole number.
- Solve multiplication problems involving unit fractions and whole numbers by using a number line and write the answer as a fraction.
- Explain how the number line model represents the multiplication of a unit fraction by a whole number in your own words.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify and count the faces, edges, and vertices of common polyhedra.
Differentiate between the altitude (height) and the slant height of a pyramid or cone.
Classify three-dimensional figures as polyhedra or non-polyhedra, and name them based on their properties.
Define and locate the base(s), lateral faces, and lateral edges of prisms and pyramids.
Identify the radius, diameter, and height of cylinders and cones.
Apply Euler's formula to verify the relationship between faces, vertices, and edges of a convex polyhedron.
Ever wonder how architects design skyscrapers or how video game designers create realistic 3D worlds? 🏙️ It all starts with understanding the basic building blocks of the shapes you see every day!
This tutorial will review the funda...
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Key Concepts & Vocabulary
TermDefinitionExample
PolyhedronA solid in three dimensions with flat polygonal faces, straight edges, and sharp corners or vertices. It has no curved surfaces.A cube is a polyhedron. A cylinder is not.
FaceA flat, polygonal surface of a polyhedron.A rectangular prism has 6 rectangular faces.
EdgeA line segment where two faces of a polyhedron meet.A cube has 12 edges of equal length.
Vertex (plural: Vertices)A point where three or more edges meet; a corner.A pyramid has a vertex at its apex where all the triangular faces meet.
Altitude (Height, h)The perpendicular distance from the base of a figure to its highest point or opposite base.The altitude of a right cylinder is the length of the segment connecting the centers of its two circular bases.
Slant Height (l)The distance from the apex...
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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. Use this to verify the parts of a polyhedron or to find a missing count if two of the three are known.
Pythagorean Theorem for Slant Height
h^2 + r^2 = l^2
In a right cone, the altitude (h), radius (r), and slant height (l) form a right triangle with the slant height as the hypotenuse. This formula is used to find a missing dimension when the other two are known. A similar principle applies to right pyramids using the apothem of the base instead of the radius.
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Challenging
A convex polyhedron has 12 vertices and 18 edges. After determining the number of faces, what is a possible name for this polyhedron?
A.Octagonal Pyramid
B.Decagonal Pyramid
C.Heptagonal Prism
D.Hexagonal Prism
Challenging
A right pyramid has a square base with a side length of 18 cm and an altitude of 12 cm. The slant height is the hypotenuse of a right triangle formed by the altitude and a line segment on the base. What is the length of that line segment on the base?
A.18 cm
B.12 cm
C.9 cm
D.6 cm
Challenging
A certain polyhedron has 'x' vertices and 'x+2' faces. If the polyhedron has 12 edges, what is the name of this polyhedron?
A.Cube
B.Tetrahedron
C.Octahedron
D.Dodecahedron
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Frequently asked questions
What grade level is "Parts of three-dimensional figures (Review)"?
Parts of three-dimensional figures (Review) is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Parts of three-dimensional figures (Review)?
You'll be able to: Draw a number line and divide it into equal parts to represent a unit fraction; Show repeated addition of a unit fraction on a number line to visually represent multiplying it by a whole number; Solve multiplication problems….
Is "Parts of three-dimensional figures (Review)" 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 Parts of three-dimensional figures (Review)?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.