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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 3

Functions and Volume

Lesson 14: Finding Cylinder Dimensions

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 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 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, Pyramids, Cylinders, Applications of 3D Geometry, Triangular Prisms and Rectangular Prisms
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 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
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 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: 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
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

In this program we explore the properties of three-dimensional figures. We do this in the context of two real-world applications. In the first, we look at the three-dimensional structure of Mayan pyramids. These stair-step structures provide a unique opportunity to also explore sequences and series. In the second application we look at the Shanghai Tower as an example of cylindrically shaped structures.

— 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.

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, Segment 1: Introduction.

We visit ancient Greece to learn about the Platonic Solids. This provides an introduction to the more general topic of three-dimensional figures.

— 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 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, Segment 2: Pyramids

Rectangular Prisms. Mayan pyramids are essentially stacks of rectangular prisms. The volume of each successive level is a percentage decrease of its lower neighbor. This introduces the notion of a geometric sequence and series, including an infinite 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, 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, 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
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
Formulas--Surface Area of a Cylinder Formulas--Surface Area of a Cylinder Formulas--Surface Area of a Cylinder

The formula for the Surface Area of a Cylinder.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

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

Surface Area and Cylinders
Formulas--Volume of a Cylinder Formulas--Volume of a Cylinder Formulas--Volume of a Cylinder

The formula for the Volume of a Cylinder.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

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

Volume and Cylinders
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: Circular Structures, Part 2 Google Earth Voyager Story: Circular Structures, Part 2 Google Earth Voyager Story: Circular Structures, Part 2

Topic

Geometric Models

Applications of Circles and Cylinders
INSTRUCTIONAL RESOURCE: Math Examples--Surface Area INSTRUCTIONAL RESOURCE: Math Examples 55 INSTRUCTIONAL RESOURCE: Math Examples--Surface Area

This set of tutorials provides an overview of the 24 worked-out examples that show how to calculate the surface area of different three-dimensional figures.

This is part of a collection of math examples for a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

Surface Area
Math Clip Art: 3D Figures--Cylinder Math Clip Art--3D Figures--Cylinder Math Clip Art--3D Figures--Cylinder

This collection of clip art images includes images of 3D figures and composite figures.

3-Dimensional Figures and Applications of 3D Geometry
Math Example--Volume Concepts--Calculating Volume: Example 1 Math Example--Volume Concepts--Calculating Volume: Example 1 Math Example--Volume Concepts--Calculating Volume: Example 1

Topic

Volume

Description

A rectangular prism with dimensions labeled: length = 30, width = 10, and height = 8. The image shows how to find the volume of the prism using the formula for volume of a rectangular prism. This image illustrates Example 1: The caption explains how to calculate the volume of the rectangular prism using the formula V = l * w * h. The given dimensions are substituted into the formula: V = 30 * 10 * 8 = 2400..

Volume
Math Example--Volume Concepts--Calculating Volume: Example 10 Math Example--Volume Concepts--Calculating Volume: Example 10 Math Example--Volume Concepts--Calculating Volume: Example 10

Topic

Volume

Description

A green cylinder with a general radius y and height x. The radius is marked on the top surface, and the height is marked on the side. This image illustrates Example 10: The task is to find the volume of this cylinder. The volume formula V = πr2h is used, and substituting r = y and h = x, the volume is calculated as V = xy2π.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 11 Math Example--Volume Concepts--Calculating Volume: Example 11 Math Example--Volume Concepts--Calculating Volume: Example 11

Topic

Volume

Description

A hollow green cylinder with an outer radius of 10 units, an inner radius of 9 units, and a height of 15 units. The radii are marked on the top surface, and the height is marked on the side. This image illustrates Example 11: The task is to find the volume of this hollow cylinder. The volume formula for a hollow cylinder V = πr12h1 - πr22h2 is used. Substituting values, the result is V = 285π.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 12 Math Example--Volume Concepts--Calculating Volume: Example 12 Math Example--Volume Concepts--Calculating Volume: Example 12

Topic

Volume

Description

A hollow green cylinder with an outer radius y, an inner radius y - 1, and a height x. The radii are marked on the top surface, and the height is marked on the side. This image illustrates Example 12: The task is to find the volume of this hollow cylinder. Using V = π(r12h1 - r22h2), substituting values gives: V = πx(y2 - (y - 1)2= πx(2y - 1).

Volume
Math Example--Volume Concepts--Calculating Volume: Example 13 Math Example--Volume Concepts--Calculating Volume: Example 13 Math Example--Volume Concepts--Calculating Volume: Example 13

Topic

Volume

Description

A rectangular-based pyramid is shown with dimensions: base length 10, base width 8, and height 30. The image demonstrates how to calculate the volume of this pyramid. This image illustrates Example 13: The caption provides a step-by-step solution for calculating the volume of a pyramid with a rectangular base using the formula V = (1/3) * Area of Base * h. Substituting values: V = (1/3) * 8 * 10 * 30 = 800.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 14 Math Example--Volume Concepts--Calculating Volume: Example 14 Math Example--Volume Concepts--Calculating Volume: Example 14

Topic

Volume

Description

A general rectangular-based pyramid is shown with variables x, y, and z representing the base dimensions and height. This example shows how to calculate the volume of a pyramid using variables instead of specific numbers. This image illustrates Example 14: The caption explains how to calculate the volume of a pyramid with a rectangular base using the formula V = (1/3) * Area of Base * h, which simplifies to V = (1/3) * x * y * z.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 15 Math Example--Volume Concepts--Calculating Volume: Example 15 Math Example--Volume Concepts--Calculating Volume: Example 15

Topic

Volume

Volume
Math Example--Volume Concepts--Calculating Volume: Example 16 Math Example--Volume Concepts--Calculating Volume: Example 16 Math Example--Volume Concepts--Calculating Volume: Example 16

Topic

Volume

Description

A truncated rectangular-based pyramid is shown with variables x, y, and z representing dimensions. The smaller virtual pyramid has reduced dimensions by 3 units for both width and length and reduced height by z - 20. The image demonstrates how to calculate the volume in terms of variables. This image illustrates Example 16: The caption explains how to find the volume of a truncated pyramid using variables for both pyramids' dimensions. Formula: V = (1/3) * xy(z + 20) - (1/3) * (y - 3)(x - 3)(z), which simplifies to V = (1/3) * (xyz + 60x + 60y - 180).

Volume
Math Example--Volume Concepts--Calculating Volume: Example 17 Math Example--Volume Concepts--Calculating Volume: Example 17 Math Example--Volume Concepts--Calculating Volume: Example 17

Topic

Volume

Description

A green sphere with a radius labeled as 3. The image is part of a math example showing how to calculate the volume of a sphere. This image illustrates Example 17: The text describes finding the volume of a sphere. The formula used is V = (4/3) * π * r3, where r = 3. After substituting, the result is V = 36π.

Volume is a fundamental concept in geometry that helps students understand the space occupied by three-dimensional objects. In this collection, each example uses various geometric shapes to calculate volume, showcasing real-life applications of volume in different shapes.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 18 Math Example--Volume Concepts--Calculating Volume: Example 18 Math Example--Volume Concepts--Calculating Volume: Example 18

Topic

Volume

Description

 

A green sphere with a radius labeled as x. This image is part of a math example showing how to calculate the volume of a sphere using an unknown radius. This image illustrates Example 18: The text explains how to find the volume of a sphere with an unknown radius x. The formula used is V = (4/3) * π * r3, and substituting r = x gives V = (4/3) * x3 * π.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 19 Math Example--Volume Concepts--Calculating Volume: Example 19 Math Example--Volume Concepts--Calculating Volume: Example 19

Topic

Volume

Description

 

A green cube with side length labeled as 7. The image illustrates how to calculate the volume of a cube with known side length. This image illustrates Example 19: The text describes finding the volume of a cube. The formula used is V = s3, where s = 7. After substituting, the result is V = 343.

Volume is a fundamental concept in geometry that helps students understand the space occupied by three-dimensional objects. In this collection, each example uses various geometric shapes to calculate volume, showcasing real-life applications of volume in different shapes.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 2 Math Example--Volume Concepts--Calculating Volume: Example 2 Math Example--Volume Concepts--Calculating Volume: Example 2

Topic

Volume

Description

A rectangular prism with dimensions labeled as x, y, and z. The image shows a general example of calculating the volume of a rectangular prism using variables instead of specific numbers. This image illustrates Example 2: The caption describes how to find the volume of a rectangular prism using variables for length (x), width (y), and height (z). The formula is given as V = x * y * z, but no specific values are provided.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 20 Math Example--Volume Concepts--Calculating Volume: Example 20 Math Example--Volume Concepts--Calculating Volume: Example 20

Topic

Volume

Description

A green cube with side length labeled as x. This image is part of a math example showing how to calculate the volume of a cube using an unknown side length. This image illustrates Example 20: The text explains how to find the volume of a cube with an unknown side length x. The formula used is V = s3, and substituting s = x gives V = x3.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 21 Math Example--Volume Concepts--Calculating Volume: Example 21 Math Example--Volume Concepts--Calculating Volume: Example 21

Topic

Volume

Description

A hollow cube with an outer edge of 9 and an inner hollow region with an edge of 7. The image shows how to calculate the volume by subtracting the volume of the inner cube from the outer cube. This image illustrates Example 21: Find the volume of a hollow cube. The formula used is V = s13 - s23, where s1 is the outer edge (9) and s2 is the inner edge (7). The solution calculates 9^3 - 7^3 = 386..

Volume
Math Example--Volume Concepts--Calculating Volume: Example 22 Math Example--Volume Concepts--Calculating Volume: Example 22 Math Example--Volume Concepts--Calculating Volume: Example 22

Topic

Volume

Description

A hollow cube with an outer edge of x and an inner hollow region with an edge of x - 2. The image shows how to calculate the volume by subtracting the volume of the inner cube from the outer cube. This image illustrates Example 22: Find the volume of a hollow cube. The formula used is V = s13 - s23, where s1 = x and s2 = x - 2. Expanding and simplifying gives V = 6x2 - 12x + 8.

Volume