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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 6 Unit 1

Reasoning to Find Area

Lesson 17: Squares and Cubes

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Nodes
Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 3: Cylinders

Closed Captioned Video: Geometry Applications: 3D Geometry, 3

Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 3: Cylinders

The Shanghai Tower in China is a stack of cylindrical shapes, where each successive layer is a percentage decrease of its lower neighbor. As with the previous section, this introduces the notion of a geometric sequence and series.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO —

Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these  figures.

Below we also include information about Platonic solids and 2D nets of these 3D figures. To get a better understanding of these 3D figures, study these basic forms.

3-Dimensional Figures, Cylinders and Applications of 3D Geometry
Closed Captioned Video: Geometry Applications: Quadrilaterals, Segment 1: Introduction

Closed Captioned Video: Geometry Applications: Quadrilaterals, 1

Closed Captioned Video: Geometry Applications: Quadrilaterals, Segment 1: Introduction

Stonehenge is best known as a circular structure. But it's the post and lintel construction used that is noteworthy, and this type of construction involves quadrilateral shapes. From the familiar door frames of houses to the majestic entryways of ancient temples, post and lintel construction provides a clear introduction to the nature of quadrilaterals. This segment also describes the key concepts developed throughout the program.

Definition of a Quadrilateral and Applications of Quadrilaterals
Closed Captioned Video: Geometry Applications: Quadrilaterals, Segment 2: Squares and Rectangles

Closed Captioned Video: Geometry Applications: Quadrilaterals, 2

Closed Captioned Video: Geometry Applications: Quadrilaterals, Segment 2: Squares and Rectangles

Frank Lloyd Wright’s architectural masterpiece Falling Water is also a stunning assembly of quadrilateral shapes. Some of the rectangular forms in this building seem to defy gravity, as we explore the properties of squares and rectangles that allowed Frank Lloyd Wright to push the envelope of design and structure.

Definition of a Quadrilateral and Applications of Quadrilaterals
Definition--3D Geometry Concepts--Antiprism

Definition--3D Geometry Concepts--Antiprism

Antiprism

Topic

3D Geometry

Definition

An antiprism is a polyhedron composed of two parallel copies of an n-sided polygon, connected by an alternating band of triangles.

Description

Antiprisms are fascinating three-dimensional geometric figures that play a significant role in the study of polyhedra and spatial geometry. Unlike prisms, which have rectangular lateral faces, antiprisms feature triangular faces connecting their two parallel polygonal bases. This unique structure gives antiprisms distinct properties and applications in various fields of mathematics and engineering.

3-Dimensional Figures
Definition. 3D Geometry Concepts--Apex

Definition--3D Geometry Concepts--Apex

Apex

Topic

3D Geometry

Definition

The apex is the highest point or vertex of a three-dimensional figure, typically opposite to and furthest from its base.

Description

In the realm of three-dimensional geometry, the concept of an apex plays a crucial role in defining and understanding various geometric solids. The apex is particularly significant in figures such as cones and pyramids, where it represents the culminating point of the structure. For a cone, the apex is the single point at the top where all the lateral lines or edges converge. In a pyramid, it's the vertex where all the triangular faces meet, forming the pinnacle of the shape.

3-Dimensional Figures
Definition. 3D Geometry Concepts--Base (Geometry)

Definition--3D Geometry Concepts--Base (Geometry)

Geometric Base in 3D Geometry

Topic

3D Geometry

Definition

A geometric base is the face of a three-dimensional figure from which the height is measured.

Description

In the context of three-dimensional geometry, the term "geometric base" is crucial for understanding the structure and properties of various 3D shapes. The base of a 3D figure is typically a flat surface, often a polygon, from which the height of the figure is perpendicular. This concept is fundamental when calculating the volume and surface area of three-dimensional shapes such as prisms, cylinders, pyramids, and cones.

3-Dimensional Figures
Definition. 3D Geometry Concepts--Cone

Definition--3D Geometry Concepts--Cone

Cone

Topic

3D Geometry

Definition

A cone is a three-dimensional geometric shape that tapers smoothly from a flat, circular base to a point called the apex or vertex.

Description

In the realm of three-dimensional geometry, a cone is a significant shape due to its unique properties and applications. A cone is characterized by a circular base and a single apex. The line segments connecting the apex to the base form a curved surface, which is known as the lateral surface of the cone. The height of the cone is the perpendicular distance from the apex to the center of the base.

Cones
Definition--3D Geometry Concepts--Cross-sections of a Cube

Definition--3D Geometry Concepts--Cross-sections of a Cube

Cross Sections of a Cube

Topic

3D Geometry

Definition

A cross-section of a cube is the intersection of a plane with the cube, resulting in a two-dimensional shape.

Description

In the study of three-dimensional geometry, understanding the cross-sections of a cube is vital for visualizing how 3D objects interact with planes. When a plane intersects a cube, the resulting shape can vary depending on the angle and position of the plane. Common cross-sections include squares, rectangles, and triangles.

Cubes
Definition--3D Geometry Concepts--Cross-Sections of a Sphere

Definition--3D Geometry Concepts--Cross-Sections of a Sphere

Cross Sections of a Sphere

Topic

3D Geometry

Definition

A cross-section of a sphere is the intersection of a plane with the sphere, resulting in a circle.

Description

In three-dimensional geometry, understanding the concept of cross-sections is crucial for visualizing and analyzing the properties of various 3D shapes. A sphere, which is a perfectly round geometrical object in three-dimensional space, can be intersected by a plane in various ways. When a plane cuts through a sphere, the shape of the intersection is always a circle. The size of this circle depends on the position of the plane relative to the center of the sphere.

Spheres
Definition--3D Geometry Concepts--Cube

Definition--3D Geometry Concepts--Cube

Cube

Topic

3D Geometry

Definition

A cube is a three-dimensional geometric figure with six equal square faces, twelve equal edges, and eight vertices.

Description

In the realm of three-dimensional geometry, the cube stands out as one of the most fundamental and symmetrical shapes. Known for its six identical square faces, a cube is a regular polyhedron, meaning all its faces are congruent squares, and all its angles are right angles. This symmetry makes the cube a crucial shape in various fields, including mathematics, architecture, and computer graphics.

Cubes
Definition--3D Geometry Concepts--Cylinder

Definition--3D Geometry Concepts--Cylinder

Cylinder

Topic

3D Geometry

Definition

A cylinder is a three-dimensional geometric figure with two parallel circular bases connected by a curved surface at a fixed distance from each other.

Description

In the realm of three-dimensional geometry, a cylinder is a fundamental shape characterized by its two identical, parallel circular bases and a curved surface that connects these bases. The line segment joining the centers of the bases is called the axis of the cylinder, and it is perpendicular to the bases. The distance between the bases is the height of the cylinder, while the radius is the distance from the center to the edge of the base.

Cylinders
Definition--3D Geometry Concepts--Edge

Definition--3D Geometry Concepts--Edge

Edge

Topic

3D Geometry

Definition

An edge in three-dimensional geometry is the line segment where two faces of a 3D shape meet.

Description

In the study of three-dimensional geometry, an edge is a fundamental concept that helps define the structure and properties of 3D shapes. Each edge is formed by the intersection of two faces, and it is a critical component in determining the overall shape and form of a 3D object. For instance, a cube has 12 edges, each formed by the meeting of two square faces.

3-Dimensional Figures
Definition--3D Geometry Concepts--Face

Definition--3D Geometry Concepts--Face

Face of a 3D Figure

Topic

3D Geometry

Definition

A face is a flat surface that forms part of the boundary of a three-dimensional figure.

Description

In the realm of three-dimensional geometry, the concept of a face is fundamental to understanding the structure and properties of 3D figures. A face represents one of the flat, two-dimensional surfaces that enclose a three-dimensional object. These surfaces play a crucial role in defining the shape, volume, and surface area of 3D figures.

3-Dimensional Figures
Definition--3D Geometry Concepts--Horizontal Cross-Sections of a Cone

Definition--3D Geometry Concepts--Horizontal Cross-Sections of a Cone

Horizontal Cross-Sections of a Cone

Topic

3D Geometry

Definition

A horizontal cross-section of a cone is the circular shape obtained when a cone is intersected by a plane that is parallel to its base.

Cones
Definition--3D Geometry Concepts--Horizontal Cross-Sections of a Cylinder

Definition--3D Geometry Concepts--Horizontal Cross-Sections of a Cylinder

Horizontal Cross Sections of a Cylinder

Topic

3D Geometry

Definition

A horizontal cross-section of a cylinder is the intersection of the cylinder with a plane that is parallel to the base of the cylinder.

Description

In the context of three-dimensional geometry, understanding the concept of cross-sections is crucial. A cylinder is a three-dimensional shape with two parallel circular bases connected by a curved surface. When a horizontal plane intersects a cylinder, the resulting cross-section is a circle. This concept is not only fundamental in geometry but also has practical applications in various fields.

Cylinders
Horizontal Cross-Sections of a Square Pyramid. A plane parallel to the base of a square pyramid creates a square cross-section

Definition--3D Geometry Concepts--Horizontal Cross-Sections of a Square Pyramid

Horizontal Cross Sections of a Square Pyramid

Topic

3D Geometry.

Definition

A horizontal cross section of a square pyramid is a two-dimensional shape obtained by slicing the pyramid with a plane parallel to its base.

Pyramids
Horizontal Cross-Sections of a Triangular Prism. A plane parallel to the base of a triangular prism creates a rectangular cross-section

Definition--3D Geometry Concepts--Horizontal Cross-Sections of a Triangular Prism

Horizontal Cross Sections of a Triangular Prism

Topic

3D Geometry

Definition

A horizontal cross-section of a triangular prism is the shape obtained by cutting the prism with a plane parallel to its base.

Description

In three-dimensional geometry, a cross-section is the intersection of a plane with a solid figure. When this plane is parallel to the base of the solid, the resulting shape is called a horizontal cross-section. For a triangular prism with a rectangular base, this cross-section will always be a rectangle, similar in shape to the base of the prism.

Triangular Prisms
Definition--3D Geometry Concepts--Net

Definition--3D Geometry Concepts--Net

Net of a 3D Figure

Topic

3D Geometry

Definition

A net is a two-dimensional shape that can be folded to form a three-dimensional figure.

Description

In the realm of three-dimensional geometry, a net is an essential concept that helps in visualizing and constructing 3D shapes. A net is essentially a two-dimensional pattern that, when folded along specific lines, forms a three-dimensional object. This concept is particularly useful in understanding the properties and structures of 3D figures such as cubes, pyramids, and prisms.

3-Dimensional Figures
Definition--3D Geometry Concepts--Net for a Cube

Definition--3D Geometry Concepts--Net for a Cube

Net for a Cube

Topic

3D Geometry

Definition

A net for a cube is a two-dimensional shape that can be folded to form a three-dimensional cube.

Description

In the realm of three-dimensional geometry, a net for a cube is a crucial concept. It represents a flattened out three-dimensional shape that can be folded along the edges to form a cube. This is an essential tool for visualizing and understanding how 3D shapes are constructed from 2D representations.

Cubes
Definition--3D Geometry Concepts--Net for a Dodecahedron

Definition--3D Geometry Concepts--Net for a Dodecahedron

Net for a Dodecahedron

Topic

3D Geometry.

Definition

A net for a dodecahedron is a two-dimensional figure that can be folded to form a three-dimensional dodecahedron.

Description

The dodecahedron is one of the five Platonic solids, characterized by its twelve regular pentagonal faces, thirty edges, and twenty vertices. Understanding the net of a dodecahedron helps in visualizing and constructing this complex polyhedron from a flat sheet.

3-Dimensional Figures
Definition--3D Geometry Concepts--Net for a Pyramid

Definition--3D Geometry Concepts--Net for a Pyramid

Net for a Pyramid

Topic

3D Geometry

Definition

A net for a pyramid is a two-dimensional representation that, when folded along its edges, forms the three-dimensional shape of a pyramid.

Description

In the study of three-dimensional geometry, understanding the concept of nets is crucial, particularly for complex shapes like pyramids. A net for a pyramid is essentially a flattened version of the 3D shape, showing all its faces in a single plane. This representation is invaluable for visualizing how the pyramid's surfaces connect and for calculating its surface area.

Pyramids
Definition--3D Geometry Concepts--Net for a Rectangular Prism

Definition--3D Geometry Concepts--Net for a Rectangular Prism

Net for a Rectangular Prism

Topic

3D Geometry

Definition

A net for a rectangular prism is a two-dimensional representation that, when folded, forms a three-dimensional rectangular prism.

Description

In the realm of three-dimensional geometry, the concept of a net is crucial for understanding how 3D shapes are constructed from 2D figures. A net for a rectangular prism is essentially a layout of all the faces of the prism in a single plane. This layout includes six rectangles that correspond to the six faces of the prism. By folding along the edges of these rectangles, one can recreate the three-dimensional shape of the rectangular prism.

Rectangular Prisms
Definition--3D Geometry Concepts--Net for a Tetrahedron

Definition--3D Geometry Concepts--Net for a Tetrahedron

Net for a Tetrahedron

Topic

3D Geometry

Definition

A net for a tetrahedron is a two-dimensional pattern that can be folded to form a three-dimensional tetrahedron, which is a polyhedron with four triangular faces.

Description

In the realm of three-dimensional geometry, the concept of a net is crucial for understanding the structure and properties of polyhedra. A tetrahedron, one of the simplest forms of polyhedra, consists of four triangular faces, six edges, and four vertices. The net of a tetrahedron is a flat, two-dimensional figure that, when folded along its edges, forms the three-dimensional shape of the tetrahedron.

3-Dimensional Figures
Definition--3D Geometry Concepts--Net for a Triangular Prism

Definition--3D Geometry Concepts--Net for a Triangular Prism

Net for a Triangular Prism

Topic

3D Geometry

Definition

A net for a triangular prism is a two-dimensional figure that can be folded to form the surface of a three-dimensional triangular prism.

Description

In the context of three-dimensional geometry, a net is a crucial concept for understanding the surface area and structure of 3D shapes. Specifically, the net for a triangular prism consists of two triangular faces and three rectangular faces. When these faces are arranged in a specific two-dimensional pattern, they can be folded along the edges to form a triangular prism.

Triangular Prisms
Definition--3D Geometry Concepts--Net for an Antiprism

Definition--3D Geometry Concepts--Net for an Antiprism

Net for an Antiprism

Topic

3D Geometry.

Definition

A net for an antiprism is a two-dimensional shape that can be folded to form a three-dimensional antiprism, which is a type of polyhedron with two parallel polygonal bases connected by an alternating band of triangles.

Description

In the realm of three-dimensional geometry, an antiprism is a fascinating polyhedron that extends the concept of prisms. Unlike regular prisms, which have two parallel bases connected by rectangular faces, antiprisms have two parallel bases connected by an alternating band of triangles. This unique structure results in a more complex and often more visually interesting shape.

3-Dimensional Figures
Definition--3D Geometry Concepts--Net for an Icosahedron

Definition--3D Geometry Concepts--Net for an Icosahedron

Net for an Icosahedron

Topic

3D Geometry

Definition

A net for an icosahedron is a two-dimensional flat pattern that, when folded along its edges, forms the surface of a three-dimensional icosahedron.

Description

The net for an icosahedron is a crucial concept in three-dimensional geometry, particularly in the study of polyhedra. An icosahedron is a regular polyhedron with 20 faces, each of which is an equilateral triangle. The net provides a visual representation of how these 20 triangular faces are connected and arranged in a flat pattern that can be folded to create the three-dimensional shape.

3-Dimensional Figures
Definition--3D Geometry Concepts--Net for an Octahedron

Definition--3D Geometry Concepts--Net for an Octahedron

Net for an Octahedron

Topic

3D Geometry

Definition

A net for an octahedron is a two-dimensional figure that can be folded to form a three-dimensional octahedron.

Description

In the realm of three-dimensional geometry, a net is a crucial concept that helps in visualizing and constructing 3D shapes from 2D representations. Specifically, a net for an octahedron consists of eight equilateral triangles arranged in a specific pattern. When these triangles are folded along the edges, they form an octahedron, which is a polyhedron with eight faces, twelve edges, and six vertices.

3-Dimensional Figures
Definition--3D Geometry Concepts--Platonic Solids

Definition--3D Geometry Concepts--Platonic Solids

Platonic Solids

Topic

3D Geometry

Definition

A Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space, where each face is a congruent regular polygon, and the same number of faces meet at each vertex.

Description

Platonic solids are fundamental constructs in the study of three-dimensional geometry. These solids are unique because they are the only five regular polyhedra that exist. Each Platonic solid has faces that are congruent regular polygons, and the same number of faces meet at each vertex, making them highly symmetrical and aesthetically pleasing. The five Platonic solids are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron, each named for its number of faces.

3-Dimensional Figures
Definition--3D Geometry Concepts--Prism

Definition--3D Geometry Concepts--Prism

Prism

Topic

3D Geometry

Definition

A prism is a three-dimensional solid object with two identical polygonal bases connected by parallelogram faces.

Description

In the realm of three-dimensional geometry, a prism is a polyhedron with two parallel, congruent bases connected by rectangular or parallelogram faces. The defining characteristic of a prism is that its cross-sections parallel to the bases are identical to the bases themselves. This property makes prisms a significant topic of study in geometry. 

3-Dimensional Figures
Definition--3D Geometry Concepts--Pyramid

Definition--3D Geometry Concepts--Pyramid

Pyramid

Topic

3D Geometry

Definition

A pyramid is a three-dimensional geometric figure with a polygonal base and triangular faces that converge to a single point called the apex.

Description

In the realm of three-dimensional geometry, a pyramid is a significant shape due to its unique properties and applications. A pyramid consists of a base that can be any polygon, such as a triangle, square, or pentagon, and triangular faces that connect each edge of the base to a single apex point. This structure results in a solid figure that is both aesthetically pleasing and structurally efficient.

Pyramids
Definition--3D Geometry Concepts--Rectangular Prism

Definition--3D Geometry Concepts--Rectangular Prism

Rectangular Prism

Topic

3D Geometry

Definition

A rectangular prism is a three-dimensional figure with six rectangular faces, where opposite faces are congruent and parallel.

Description

The rectangular prism is a fundamental shape in three-dimensional geometry, serving as a building block for understanding more complex 3D structures. It is characterized by its three dimensions: length, width, and height, which are clearly labeled in the image. This shape is ubiquitous in both natural and man-made environments, making it a crucial concept for students to grasp.

Rectangular Prisms
Definition--3D Geometry Concepts--Slant Height

Definition--3D Geometry Concepts--Slant Height

Slant Height

Topic

3D Geometry

Definition

Slant height is the distance measured along a lateral face from the base to the apex of a three-dimensional figure, such as a pyramid or a cone.

Description

In the context of three-dimensional geometry, the slant height is a crucial measurement for various solid figures, particularly right pyramids and right circular cones. It represents the shortest path along the surface of the figure from the apex (top point) to the base, distinguishing it from the vertical height which measures the perpendicular distance from the apex to the center of the base.

3-Dimensional Figures
Definition--3D Geometry Concepts--Sphere

Definition--3D Geometry Concepts--Sphere

Sphere

Topic

3D Geometry

Definition

A sphere is a perfectly round three-dimensional geometric object in which every point on the surface is equidistant from the center.

Description

In the realm of three-dimensional geometry, a sphere is a fundamental shape characterized by its symmetry and uniformity. It is defined mathematically as the set of all points in space that are at a constant distance, known as the radius, from a fixed point called the center. This distance is the same in all directions, making the sphere a unique object with no edges or vertices.

Spheres
Definition--3D Geometry Concepts--Square Pyramid

Definition--3D Geometry Concepts--Square Pyramid

Square Pyramid

Topic

3D Geometry

Definition

A square pyramid is a three-dimensional geometric figure with a square base and four triangular faces that converge at a single point called the apex.

Pyramids
Definition--3D Geometry Concepts--Surface Area

Definition--3D Geometry Concepts--Surface Area

Surface Area of 3D Figures

Topic

3D Geometry

Definition

Surface area is the total area that the surface of a three-dimensional object occupies.

Description

In the realm of three-dimensional geometry, surface area is a fundamental concept that quantifies the extent of a 3D shape's exterior surface. This measure is crucial for various applications, including engineering, architecture, and everyday tasks. For example, when painting a room, the surface area of the walls, ceiling, and floor must be calculated to determine the amount of paint required.

Surface Area
Definition--3D Geometry Concepts--Triangular Prism

Definition--3D Geometry Concepts--Triangular Prism

Triangular Prism

Topic

3D Geometry

Definition

A triangular prism is a three-dimensional geometric solid with two congruent triangular bases and three rectangular faces.

Description

The triangular prism is a fundamental shape in three-dimensional geometry, playing a crucial role in understanding the properties of polyhedra and their applications in various fields. This prism is characterized by its unique structure, consisting of two parallel triangular bases connected by three rectangular faces. The shape of the triangular bases can vary, allowing for right, equilateral, isosceles, or scalene triangular prisms.

Triangular Prisms
Definition--3D Geometry Concepts--Triangular Pyramid

Definition--3D Geometry Concepts--Triangular Pyramid

Triangular Pyramid

Topic

3D Geometry

Definition

A triangular pyramid, also known as a tetrahedron, is a three-dimensional geometric figure with four triangular faces, six edges, and four vertices.

Description

In the realm of three-dimensional geometry, the triangular pyramid holds significant relevance due to its unique properties and structural simplicity. Each triangular face of the pyramid converges at a single point known as the apex, forming a solid figure that is both symmetrical and aesthetically pleasing. This geometric shape is the simplest form of a pyramid and is often used in various fields such as architecture, molecular chemistry, and computer graphics.

Pyramids
Definition--3D Geometry Concepts--Vertex

Definition--3D Geometry Concepts--Vertex

Vertex in 3D Geometry

Topic

3D Geometry

Definition

A vertex is a point where three or more edges meet in a three-dimensional figure.

Description

In the study of three-dimensional geometry, the term vertex is fundamental. A vertex is a critical point in any 3D geometric shape, marking the intersection of edges. For example, in a cube, each corner where the edges converge is a vertex. Vertices are essential in defining the shape and structure of 3D figures, as they help in understanding the spatial relationships between different parts of the figure.

3-Dimensional Figures
Vertical Cross-Sections of a Cone. A plane perpendicular to the base of a cone and crossing the apex creates a triangular cross-section

Definition--3D Geometry Concepts--Vertical Cross-Sections of a Cone

Vertical Cross Sections of a Cone

Topic

3D Geometry

Definition

A vertical cross section of a cone is the intersection of the cone with a plane that passes through its vertex and base, resulting in a two-dimensional shape.

Cones
Vertical Cross-Sections of a Cylinder. A plane parallel to the side of a cylinder creates a rectangular cross-section

Definition--3D Geometry Concepts--Vertical Cross-Sections of a Cylinder

Vertical Cross Sections of a Cylinder

Topic

3D Geometry

Definition

A vertical cross-section of a cylinder is the intersection of the cylinder with a plane that is parallel to its axis. This cross-section is typically a rectangle if the plane cuts through the entire height of the cylinder.

Cylinders
Vertical Cross-Sections of a Square Pyramid. A plane perpendicular to the base of a square pyramid and crossing the apex creates a triangular cross-section

Definition--3D Geometry Concepts--Vertical Cross-Sections of a Square Pyramid

Vertical Cross Sections of a Square Pyramid

Topic

3D Geometry

Definition

A vertical cross section of a square pyramid is the intersection of the pyramid with a vertical plane that passes through its apex and base, resulting in a two-dimensional shape.

Pyramids
Vertical Cross-Sections of a Triangular Prism. A plane perpendicular to the base of a triangular prism creates a triangular cross-section

Definition--3D Geometry Concepts--Vertical Cross-Sections of a Triangular Prism

Vertical Cross Sections of a Triangular Prism

Topic

3D Geometry

Definition

A vertical cross section of a triangular prism is a two-dimensional shape obtained by slicing the prism parallel to its height, revealing a triangular face.

Triangular Prisms
Definition--3D Geometry Concepts--Volume

Definition--3D Geometry Concepts--Volume

Volume

Topic

3D Geometry

Definition

Volume is the measure of the amount of space occupied by a three-dimensional object, expressed in cubic units.

Description

Volume is a fundamental concept in the study of three-dimensional geometry. It quantifies the capacity of a 3D object, indicating how much space it occupies. This measurement is crucial in various fields, including mathematics, engineering, architecture, and physical sciences.

Volume
Definition--3D Geometry Concepts--Cavalieri's Principle

Definition--3D Geometry Concepts--Cavalieri's Principle

Cavalieri's Principle

Topic

3D Geometry

Definition

Cavalieri's Principle states that if two solids are contained between two parallel planes, and every plane parallel to these planes intersects both solids in cross-sections of equal area, then the two solids have equal volumes.

Description

Cavalieri's Principle is a fundamental concept in three-dimensional geometry that provides a method for determining the volume of solids. Named after the Italian mathematician Bonaventura Cavalieri, this principle is particularly useful for comparing the volumes of solids that might not have straightforward geometric shapes.

3-Dimensional Figures
Geometry Applications Teachers Guide: 3D Geometry

Geometry Applications Teachers Guide: 3D Geometry

Geometry Applications Teachers Guide: 3D Geometry

This is the Teacher's Guide that accompanies Geometry Applications: 3D Geometry.

This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Applications of 3D Geometry
Google Earth Voyager Story: The Geometry of Sustainable Architecture, Part 2

Google Earth Voyager Story: The Geometry of Sustainable Architecture, Part 2

Google Earth Voyager Story: The Geometry of Sustainable Architecture, Part 2

Topic

Geometric Models

Surface Area, Volume and Rational Functions and Equations
Google Earth Voyager Story: The Mathematics of Pyramids, Part 1

Google Earth Voyager Story: The Mathematics of Pyramids, Part 1

Google Earth Voyager Story: The Mathematics of Pyramids, Part 1

Topic

Geometric Models

Pyramids
Google Earth Voyager Story: The Mathematics of Pyramids, Part 2

Google Earth Voyager Story: The Mathematics of Pyramids, Part 2

Google Earth Voyager Story: The Mathematics of Pyramids, Part 2

Topic

Geometric Models

Pyramids
Interactive Crossword Puzzle--Quadrilaterals

Interactive Crossword Puzzle--Quadrilaterals

Interactive Crossword Puzzle--Quadrilaterals

This interactive crossword puzzle tests knowledge of key terms on the topic of quadrilaterals.

This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.
Definition of a Quadrilateral
Interactive Math Game--Memory Game, 3D Figures

Interactive Math Game--Memory Game: 3D Figures

Interactive Math Game--Memory Game: 3D Figures

Use this math game to review 3D figures. This is a Memory-style game in which students must remember the location of pairs of identical images.

This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.
3-Dimensional Figures