Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 3

Functions and Volume

Lesson 13: The Volume of a Cylinder

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Collection Holiday Themed Resource Collection: Math in the News  

This is a collection of Holiday-Themed issues of Math in the News.

 

Data Analysis, Applications of Exponential and Logarithmic Functions, Surface Area and Volume
Math in the News Math in the News Collection: Applications of Surface Area and Volume

Overview

This is a collection of issues of Math in the News that deal with applications of Surface Area and Volume.

 

 

 
Surface Area and Volume
Math in the News Math in the News Collection: Applications of 3D Geometry

Overview

This is a collection of issues of Math in the News that deal with applications of 3D geometry.

 

 

 
3-Dimensional Figures and Applications of 3D Geometry
Math in the News Math in the News Collection: Business Math

Overview

This is a collection of issues of Math in the News that deal with business applications.

 

 

 
Applications of Exponential and Logarithmic Functions, Data Analysis and Volume
Math in the News Math in the News Collection: Applications of Data Analysis

Overview

This is a collection of Math in the News stories that focus on the topic of Data Analysis.

 

 

 
Data Analysis, Data Gathering, Probability, Percents and Ratios and Rates
Circles Collection Math Definitions Collection: Circles

Overview

The collection of definitions on the topic of circles provided by Media4Math is an invaluable resource for students and educators alike. This comprehensive set includes essential terms such as radius, diameter, circumference, chord, and tangent, each explained with clarity and precision. Understanding these fundamental concepts is crucial for students as they form the building blocks for more advanced studies in geometry and algebra.

Definition of a Circle
Math Videos Math Video Collection: 3D Geometry Animations

Overview

This collection aggregates all the math videos and resources in this series: 3D Geometry Animations. There are a total of 10 resources. This collection of resources is made up of downloadable MP4, transcripts, and other resources files that you can easily incorporate into a presentation.

 

3-Dimensional Figures, Cubes, Cones, Triangular Prisms, Pyramids, Cylinders and Rectangular Prisms
Math Videos Math Video Collection: Geometry Applications Video Series: Circles

Overview

This collection aggregates all the math videos and resources in this series: Geometry Applications Video Series: Circles. There are a total of 13 resources. This collection of resources is made up of downloadable MP4, transcripts, and other resources files that you can easily incorporate into a presentation.

 

Applications of Circles and Definition of a Circle
Math Videos Math Video Collection: Geometry Applications Video Series: 3D Geometry

Overview

This collection aggregates all the math videos and resources in this series: Geometry Applications Video Series: 3D Geometry. There are a total of 18 resources. This collection of resources is made up of downloadable MP4, transcripts, and other resources files that you can easily incorporate into a presentation.

 

3-Dimensional Figures, Applications of 3D Geometry, Pyramids, Cylinders, Rectangular Prisms and Triangular Prisms
Math Examples Math Examples Collection: Volume

Overview

This collection of math examples on the topic of Volume provides students with an in-depth exploration of volume concepts through a variety of visual models. Covering a range of skills and increasing in complexity, this collection helps students master foundational and advanced topics in volume. From calculating the volume of basic geometric shapes to applying volume formulas to complex objects, these examples build confidence and enhance comprehension by breaking down challenging concepts visually.

Volume
Math Examples Math Examples Collection: Modeling Volume

Overview

This collection of math examples on the topic of Volume provides a comprehensive approach to understanding and mastering volume calculations. These examples increase in complexity and cover a range of essential skills, from basic volume calculations of simple shapes to more advanced composite figures. Using visual models, these examples simplify complex concepts, helping students grasp the intricacies of volume calculation through clear, engaging representations.

Volume
Math Examples Math Examples Collection: Circular Area and Circumference

Overview

This collection aggregates all the math examples around the topic of Circular Area and Circumference. There are a total of 23 Math Examples. This collection of resources is made up of downloadable PNG images that you can easily incorporate into your lesson plans.
Area and Circumference
VIDEO: 3D Geometry Animation: Antiprism VIDEO: 3D Geometry Animation: Antiprism VIDEO: 3D Geometry Animation: Antiprism

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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 and Triangular Prisms
VIDEO: 3D Geometry Animation: Cone VIDEO: 3D Geometry Animation: Cone VIDEO: 3D Geometry Animation: Cone

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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 and Cones
VIDEO: 3D Geometry Animation: Cube VIDEO: 3D Geometry Animation: Cube VIDEO: 3D Geometry Animation: Cube

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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 and Cubes
VIDEO: 3D Geometry Animation: Cylinder VIDEO: 3D Geometry Animation: Cylinder 3D Geometry Animation: Cylinder

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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 and Cylinders
VIDEO: 3D Geometry Animation: Octahedron VIDEO: 3D Geometry Animation: Octahedron VIDEO: 3D Geometry Animation: Octahedron

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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
VIDEO: 3D Geometry Animation: Pyramid VIDEO: 3D Geometry Animation: Pyramid VIDEO: 3D Geometry Animation: Pyramid

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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 and Pyramids
VIDEO: 3D Geometry Animation: Rectangular Prism VIDEO: 3D Geometry Animation: Rectangular Prism VIDEO: 3D Geometry Animation: Rectangular Prism

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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 and Rectangular Prisms
VIDEO: 3D Geometry Animation: Tetrahedron VIDEO: 3D Geometry Animation: Tetrahedron VIDEO: 3D Geometry Animation: Tetrahedron

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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
VIDEO: 3D Geometry Animation: Triangular Prism VIDEO: 3D Geometry Animation: Triangular Prism VIDEO: 3D Geometry Animation: Triangular Prism

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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
Animated Math Clip Art--3D Geometry--Cube with Horizontal Cross-Section Animated Math Clip Art--3D Geometry--Cube with Horizontal Cross-Section Cube with Horizontal Cross-Section

Topic

3D Geometry

Description

This animation shows a cube with a horizontal cross-section, illustrating how slicing the cube parallel to its base results in a square cross-section. This is useful for visualizing and understanding the internal structure and symmetry of cubes.

Using animated math clip art like this helps students visualize the concept of cross-sections and their applications in geometry. Teachers can use this image to explain how horizontal cross-sections reveal the internal structure of cubes.

3-Dimensional Figures
Animated Math Clip Art--3D Geometry--Dodecahedron Animated Math Clip Art--3D Geometry--Dodecahedron Dodecahedron

Topic

3D Geometry

Description

A dodecahedron is a three-dimensional shape with twelve flat faces, each a regular pentagon. This animated clip art shows the rotation of a dodecahedron, highlighting its symmetry and geometric properties.

Animated math clip art like this is crucial for teaching as it allows students to visualize complex polyhedra, enhancing their understanding of geometric concepts. Teachers can use this image to explain the structure and characteristics of dodecahedrons.

Here is a potential script for teachers: "Today, we are going to explore the geometry of a dodecahedron. Notice how the twelve pentagonal faces form a symmetrical shape. This helps us understand the properties of polyhedra."

3-Dimensional Figures
Animated Math Clip Art--3D Geometry--Rotating a Rectangle to Form a Cylinder Rotating a Rectangle to Form a Cylinder

Topic

3D Geometry

Description

This animation demonstrates how rotating a rectangle around one of its sides creates a cylinder. It's a powerful visualization of how 2D shapes can generate 3D objects through rotation.

Using animated math clip art like this helps students understand the concept of solids of revolution. Teachers can use this to introduce topics in calculus, such as finding volumes using the disk or washer methods.

Cylinders
Animated Clip Art Animated Math Clip Art--3D Geometry--Rotating a Rectangle to Form an Open Cylinder Rotating a Rectangle to Form an Open Cylinder

Topic

3D Geometry

Description

This animation shows how rotating a rectangular strip around an axis parallel to one of its sides creates an open cylinder. It illustrates the concept of surface area of revolution.

Animated math clip art like this is valuable for teaching as it helps students visualize how 2D shapes can generate 3D surfaces. Teachers can use this to introduce topics in calculus, such as finding surface areas of revolution.

Cylinders
Animated Math Clip Art--3D Geometry--Rotating a Square to Form a Cylinder Rotating a Square to Form a Cylinder

Topic

3D Geometry

Description

This animation demonstrates how rotating a square around one of its sides creates a cylinder. It's a special case of rotating a rectangle, where the height and diameter of the resulting cylinder are equal.

Using animated math clip art like this helps students understand the relationship between 2D and 3D shapes. Teachers can use this to discuss how the dimensions of the original shape relate to the dimensions of the resulting solid.

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

Topic

3D Geometry

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

Topic

3D Geometry

Description

Description: This segment introduces Platonic solids, including tetrahedron, cube, and dodecahedron, emphasizing their congruent edges, vertices, and angles. It connects these geometric figures to both natural and man-made structures, setting the stage for exploring 3D geometry applications.

3-Dimensional Figures and Applications of 3D Geometry
Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 2: Pyramids Closed Captioned Video: Geometry Applications: 3D Geometry, 2 Closed Captioned Video: Geometry Applications: 3D Geometry, 2

Topic

3D Geometry

Description

Description: This segment explores pyramids, particularly Mayan and Egyptian structures, to distinguish rectangular and square bases. It discusses the volume of truncated pyramids using proportional relationships and introduces the concept of tiered volume reduction through geometric sequences.

3-Dimensional Figures, Pyramids and Applications of 3D Geometry
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, 3

Topic

3D Geometry

Description

Description: This segment examines cylinders, using the Shanghai Tower as a case study. It highlights how adjustments to height and radius affect volume and surface area, demonstrating these principles with geometric calculations and their architectural applications in energy efficiency.

3-Dimensional Figures, Cylinders and Applications of 3D Geometry
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--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
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
Definition--Circle Concepts--Arc Length Definition--Circle Concepts--Arc Length Arc Length

Topic

Circles

Definition

An arc length is the distance along the curved line making up the arc.

Description

The arc length is a crucial concept in geometry, particularly when dealing with circles. It is calculated using the formula 

L = rθ

Definition of a Circle
Definition--Circle Concepts--Area of a Circle Definition--Circle Concepts--Area of a Circle Area of a Circle

Topic

Circles

Definition

The area of a circle is the space contained within its circumference, calculated as 

A = πr2

Description

The area of a circle is a fundamental concept in geometry, representing the space enclosed by the circle's boundary. This concept is widely applicable in fields such as physics, engineering, and design, where understanding the area is crucial for tasks like calculating material quantities or designing circular components. The formula 

A = πr2 

Definition of a Circle
Definition--Circle Concepts--Center of a Circle Definition--Circle Concepts--Center of a Circle Center of a Circle

Topic

Circles

Definition

The center of a circle is the point equidistant from all points on the circle.

Description

The center of a circle is a pivotal concept in geometry, serving as the reference point from which the radius is measured. It is crucial in defining the circle's position in a plane and is used in various applications such as navigation, where the center can represent a central point of rotation or balance. In mathematical terms, the center is often denoted as the point (h , k) in the Cartesian coordinate system, where all points on the circle satisfy the equation 

Definition of a Circle
Definition--Circle Concepts--Chord Definition--Circle Concepts--Chord Chord

Topic

Circles

Definition

A chord is a line segment with both endpoints on the circle.

Definition of a Circle
Definition--Circle Concepts--Circle Definition--Circle Concepts--Circle Circle

Topic

Circles

Definition

A circle is a set of all points in a plane equidistant from a given point, the center.

Description

The circle is one of the most fundamental shapes in geometry, characterized by its symmetry and uniformity. It is used extensively in various fields, including engineering, design, and astronomy, where its properties are applied to create wheels, gears, and orbits. Mathematically, a circle is defined by its center and radius, and its equation in a plane is 

(x − h)2 + (y − k)2 = r2 

Definition of a Circle
Definition--Circle Concepts--Circle Inscribed in a Square Definition--Circle Concepts--Circle Inscribed in a Square Circle Inscribed in a Square

Topic

Circles

Definition

A circle inscribed in a square touches all four sides of the square at exactly one point each.

Definition of a Circle
Definition--Circle Concepts--Circle Inscribed in a Triangle Definition--Circle Concepts--Circle Inscribed in a Triangle Circle Inscribed in a Triangle

Topic

Circles

Definition

An inscribed circle in a triangle is tangent to each of the triangle's sides.

Definition of a Circle
Definition--Circle Concepts--Circles on a Coordinate Plane Definition--Circle Concepts--Circles on a Coordinate Plane Circles on a Coordinate Plane

Topic

Circles

Definition

Circles on a coordinate plane are defined by their center coordinates and radius.

Description

Understanding circles on a coordinate plane is essential for analyzing geometric shapes in a mathematical context. This concept is widely used in computer graphics, navigation systems, and physics simulations, where precise positioning and movement of circular objects are required. The standard equation of a circle in the coordinate plane is 

(x − h)2 + (y − k)2 = r2

Definition of a Circle
Definition--Circle Concepts--Circular Arc Definition--Circle Concepts--Circular Arc Circular Arc

Topic

Circles

Definition

A circular arc is a portion of the circumference of a circle.

Description

Circular arcs are segments of a circle's circumference, used extensively in design, architecture, and engineering to create curved structures and paths. The length of an arc is determined by the central angle and the circle's radius, calculated using the formula 

L = rθ

Definition of a Circle
Definition--Circle Concepts--Circular Composite Figures Definition--Circle Concepts--Circular Composite Figures Circular Composite Figures

Topic

Circles

Definition

Circular composite figures are shapes that include circles or parts of circles combined with other geometric figures.

Definition of a Circle
Definition--Circle Concepts--Circular Cross-Sections Definition--Circle Concepts--Circular Cross-Sections Circular Cross-Sections

Topic

Circles

Definition

Circular cross-sections are the intersections of a plane with a solid that result in a circle.

Definition of a Circle
Definition--Circle Concepts--Circular Functions Definition--Circle Concepts--Circular Functions Circular Functions

Topic

Circles

Definition

Circular functions are trigonometric functions that relate angles to ratios of sides in a right triangle.

Definition of a Circle
Definition--Circle Concepts--Circular Models Definition--Circle Concepts--Circular Models Circular Models

Topic

Circles

Definition

Circular models are representations of circular phenomena using mathematical equations and diagrams.

Definition of a Circle
Definition--Circle Concepts--Circular Numerical Models Definition--Circle Concepts--Circular Numerical Models Circular Numerical Models

Topic

Circles

Definition

Circular numerical models use numerical methods to analyze and simulate circular phenomena.

Definition of a Circle
Definition--Circle Concepts--Circumcenter of Triangle Definition--Circle Concepts--Circumcenter of Triangle Circumcenter of Triangle

Topic

Circles

Definition

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect, equidistant from the vertices.

Definition of a Circle
Definition--Circle Concepts--Circumference Definition--Circle Concepts--Circumference Circumference

Topic

Circles

Definition

The circumference of a circle is the distance around the circle, calculated as C = 2πr.

Description

The circumference is a fundamental concept in geometry, representing the perimeter of a circle. It is widely used in fields such as engineering, design, and manufacturing, where precise measurements of circular objects are required. The formula 

C = 2πr 

Definition of a Circle
Definition--Circle Concepts--Circumscribed Angle Definition--Circle Concepts--Circumscribed Angle Circumscribed Angle

Topic

Circles

Definition

A circumscribed angle is an angle formed outside a circle by two intersecting tangents.

Definition of a Circle