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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 3

Functions and Volume

Lesson 15: The Volume of a Cone

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
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: 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 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
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 Animated Math Clip Art--3D Geometry--Rotating a Triangle to Form a Cone Rotating a Triangle to Form a Cone

Topic

3D Geometry

Description

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

Animated math clip art like this is crucial for teaching as it helps students visualize the formation of cones. Teachers can use this to introduce concepts of volume and surface area of cones, as well as topics in calculus related to solids of revolution.

Cones
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
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
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 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
Math Example--Volume Concepts--Calculating Volume: Example 23 Math Example--Volume Concepts--Calculating Volume: Example 23 Math Example--Volume Concepts--Calculating Volume: Example 23

Topic

Volume

Description

 

A cone with a height of 12 and a radius of 4. The image shows how to calculate its volume using the cone volume formula (V = 1/3 * π * r2 * h). This image illustrates Example 23: Find the volume of a cone. The formula used is V = (1/3) * π * r2 * h, where r = 4 and h = 12. Substituting these values gives V = (1/3) * π * (42) * 12 = 64π.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 24 Math Example--Volume Concepts--Calculating Volume: Example 24 Math Example--Volume Concepts--Calculating Volume: Example 24

Topic

Volume

Description

A cone with a height labeled as y and a radius labeled as x. The image shows how to calculate its volume using the cone volume formula (V = 1/3 * π * r2 * h). This image illustrates Example 24: Find the volume of a cone. The formula used is V = (1/3) * π * r2 * h, where r = x and h = y. Substituting these variables gives V = (x^2 * y)/3 * π.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 3 Math Example--Volume Concepts--Calculating Volume: Example 3 Math Example--Volume Concepts--Calculating Volume: Example 3

Topic

Volume

Description

A hollow rectangular prism with outer dimensions: length = 60, width = 20, and height = 16. The inner hollow part has dimensions: length = 60, width = 18, and height = 14. The image shows how to subtract volumes to find the hollow volume. This image illustrates Example 3: The caption explains how to calculate the volume of a hollow rectangular prism by subtracting the inner volume from the outer volume. V = (60 * 20 * 16) - (60 * 18 * 14) = 4080.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 4 Math Example--Volume Concepts--Calculating Volume: Example 4 Math Example--Volume Concepts--Calculating Volume: Example 4

Topic

Volume

Description

A hollow rectangular prism with outer dimensions labeled as x, y, and z, and inner hollow dimensions labeled as x - 2 and y - 2. The image shows a symbolic calculation for finding the hollow volume using variables. This image illustrates Example 4: The caption describes how to calculate the volume of a hollow rectangular prism by subtracting the inner volume from the outer volume using variables: V = xyz - z(y - 2)(x - 2) = 2z(y + x - 2).

Volume
Math Example--Volume Concepts--Calculating Volume: Example 5 Math Example--Volume Concepts--Calculating Volume: Example 5 Math Example--Volume Concepts--Calculating Volume: Example 5

Topic

Volume

Description

The image shows a triangular prism with dimensions labeled as base (7), height (10), and length (25). It is part of an example on how to calculate the volume of a solid triangular prism. This image illustrates Example 5: "Find the volume of this triangular prism." The solution involves substituting the given measurements into the volume formula for a triangular prism: V = 1/2 * b * h * l = 1/2 * 7 * 10 * 25 = 875.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 6 Math Example--Volume Concepts--Calculating Volume: Example 6 Math Example--Volume Concepts--Calculating Volume: Example 6

Topic

Volume

Description

The image depicts a triangular prism with dimensions labeled as x, y, and z. The example demonstrates how to calculate the volume using a general formula for a triangular prism. This image illustrates Example 6: "Find the volume of this triangular prism." The solution uses the formula V = 1/2 * b * h * l, which is simplified to V = 1/2 * x * y * z..

Volume
Math Example--Volume Concepts--Calculating Volume: Example 7 Math Example--Volume Concepts--Calculating Volume: Example 7 Math Example--Volume Concepts--Calculating Volume: Example 7

Topic

Volume

Description

The image shows a hollow triangular prism with outer dimensions labeled as base (10), height (7), and length (35), and inner dimensions labeled as base (8) and height (5). The example calculates the volume by subtracting the hollow region from the full prism. This image illustrates Example 7: "Find the volume of this hollow triangular prism." The solution calculates the full volume using V = 1/2 * b1 * h1 * l1 - 1/2 * b2 * h2 * l2, which simplifies to V = 1/2 * 10 * 7 * 35 - 1/2 * 8 * 5 * 35 = 525..

Volume
Math Example--Volume Concepts--Calculating Volume: Example 8 Math Example--Volume Concepts--Calculating Volume: Example 8 Math Example--Volume Concepts--Calculating Volume: Example 8

Topic

Volume

Description

This image shows a hollow triangular prism with outer dimensions labeled as x, y, and z, and inner dimensions reduced by 2 units each. It demonstrates how to calculate the volume by subtracting the hollow region from the full prism. This image illustrates Example 8: "Find the volume of this hollow triangular prism." The solution uses V = 1/2 * b1 * h1 * l1 - 1/2 * b2 * h2 * l2, which simplifies to V = z(xy - (x - 2)(y - 2)) = z(x + y - 2)..

Volume
Math Example--Volume Concepts--Calculating Volume: Example 9 Math Example--Volume Concepts--Calculating Volume: Example 9 Math Example--Volume Concepts--Calculating Volume: Example 9

Topic

Volume

Description

 

A green cylinder with a radius of 10 units and a height of 8 units. The radius is marked on the top surface, and the height is marked on the side. This image illustrates Example 9: The task is to find the volume of the cylinder. The volume formula V = πr2h is used. Substituting the values r = 10 and h = 8, the volume is calculated as V= 800π.

Volume
MATH EXAMPLES--Teacher's Guide: Surface Area MATH EXAMPLES--Teacher's Guide: Surface Area MATH EXAMPLES--Teacher's Guide: Surface Area

This Teacher's Guide 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 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.

Surface Area
MATH EXAMPLES--Teacher's Guide: Volume MATH EXAMPLES--Teacher's Guide: Volume MATH EXAMPLES--Teacher's Guide: Volume

This set of tutorials provides 24 examples of how to find the volume of various 3-dimensional geometric figures.

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.

Volume