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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
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
MATH EXAMPLES--Volume MATH EXAMPLES--Volume MATH EXAMPLES--Volume

This set of tutorials provides 24 examples of how to find the volume of various 3-dimensional geometric figures. NOTE: The download is a PPT file.

Volume
Math in the News: Issue 13--Living Near Volcanoes Math in the News: Issue 13--Living Near Volcanoes Math in the News: Issue 13--Living Near Volcanoes

6/13/11. In this issue we explore the volcanic eruption in Chile that resulted in a huge plume of smoke and ash that was miles high. We explore the viscosity of lava that makes such eruptions possible.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Volume
Math in the News: Issue 15--Fracking for Oil Math in the News: Issue 15--Fracking for Oil Math in the News: Issue 15--Fracking for Oil

6/27/11. In this issue we look at the technology of hydraulic fracking. In particular, we estimate the amount of drilling required for such wells.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Volume
Math in the News: Issue 20--Heat Wave! Math in the News: Issue 20--Heat Wave! Math in the News: Issue 20--Heat Wave!

8/1/11. In this issue we look at the physics of air pressure and the forces that give rise to heat waves.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Data Analysis
Math in the News: Issue 27--Emerging from the Ashes of 9/11 Math in the News: Issue 27--Emerging from the Ashes of 9/11 Math in the News: Issue 27--Emerging from the Ashes of 9/11

9/19/11. To commemorate the 10-year anniversary of the 911, we look at the geometry and architecture of the Freedom Tower, currently under construction.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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3-Dimensional Figures
Math in the News: Issue 35--125 and Counting Math in the News: Issue 35--125 and Counting Math in the News: Issue 35--125 and Counting

11/14/11. In this issue we commemorate the 125th anniversary of the Statue of Liberty. We also look at the geometry and architecture of this monument.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Surface Area and Volume
Math in the News: Issue 37--A Parade of Geometry Math in the News: Issue 37--A Parade of Geometry Math in the News: Issue 37--A Parade of Geometry

11/28/11. In this issue we look at the geometry of parade balloons.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Surface Area and Volume
Math in the News: Issue 38--December 7, 1941 Math in the News: Issue 38--December 7, 1941 Math in the News: Issue 38--December 7, 1941

12/7/11. In this issue we look at the heroic work of salvaging and retrofitting many of the ships sunk during the attack on Pearl Harbor.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Surface Area and Volume
Math in the News: Issue 39--Monument to a Hero Math in the News: Issue 39--Monument to a Hero Math in the News: Issue 39--Monument to a Hero

12/12/11. In this issue we look at the MLK Memorial and the special properties of granite that presented some design challenges in the construction of the statue.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Surface Area and Volume
Math in the News: Issue 44--Sunk: The Costa Concordia Math in the News: Issue 44--Sunk: The Costa Concordia Math in the News: Issue 44--Sunk: The Costa Concordia

January 2012. In this issue of Math in the News we analyze how the Costa Concordia sank.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Surface Area and Volume
Math in the News: Issue 53--Titanic: A Century Later Math in the News: Issue 53--Titanic: A Century Later Math in the News: Issue 53--Titanic: A Century Later

April 2012. In this issue of Math in the News we analyze the sinking of the Titanic. It has been a hundred years, yet the story of the sinkin g of the Titanic still fascinates.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Surface Area and Volume
Math in the News: Issue 56--The Freedom Tower Math in the News: Issue 56--The Freedom Tower Math in the News: Issue 56--The Freedom Tower

May 2012. In this issue of Math in the News we look at the architecture of the Freedom Tower, now that it has become the tallest building in NYC.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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3-Dimensional Figures
Math in the News: Issue 73--County Fairs and Funnel Cakes Math in the News: Issue 73--County Fairs and Funnel Cakes Math in the News: Issue 73--County Fairs and Funnel Cakes

August 2013. In this issue we look at the geometry of funnel cakes. You'll like the sweet results.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Surface Area and Volume
Math in the News: Issue 8--Tornado Damage Math in the News: Issue 8--Tornado Damage Math in the News: Issue 8--Tornado Damage

5/9/11. In this issue we look at tornado season. In particular we study why the swirling winds of a tornado are so damaging.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Data Analysis
Math in the News: Issue 9--Mississippi Floods Math in the News: Issue 9--Mississippi Floods Math in the News: Issue 9--Mississippi Floods

5/16/11. In this issue we look at the flooding along the Mississippi. In particular we analyze the flooding along Memphis, Tennessee. We develop a model for predicting the amount of flooding.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Volume
Promethean Flipchart: Geometry Applications: 3D Geometry 1

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. Note: The download for this resources is the Promethean Flipchart.

For access to the full video [Geometry Applications: 3D Geometry, Segment 2: Pyramids]: https://media4math.com/library/geometry-applications-3d-geometry-segment-2-pyramids

This video includes a Video Transcript [Video Transcript: Geometry Applications: 3D Geometry, Segment 2: Pyramids]: https://www.media4math.com/library/video-transcript-geometry-applications-3d-geometry-segment-2-pyramids

Applications of 3D Geometry
Promethean Flipchart: Geometry Applications: 3D Geometry 2

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. Note: The download for this resources is the Promethean Flipchart.

To access the full video [Geometry Applications: 3D Geometry, Segment 3: Cylinders]: https://media4math.com/library/geometry-applications-3d-geometry-segment-3-cylinders

This video includes a Video Transcript [Video Transcript: Geometry Applications: 3D Geometry, Segment 3: Cylinders]: https://www.media4math.com/library/video-transcript-geometry-applications-3d-geometry-segment-3-cylinders

 

Applications of 3D Geometry
Video Definition 14--3D Geometry--Horizontal Cross-Section of a Cylinder Video Definition 14--3D Geometry--Horizontal Cross-Section of a Cylinder Horizontal Cross-Section of a Cylinder

Topic

3D Geometry

Definition

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

Cylinders
Video Definition 14--3D Geometry--Horizontal Cross-Section of a Cylinder--Spanish Audio Video Definition 14--3D Geometry--Horizontal Cross-Section of a Cylinder--Spanish Audio Video Definition 14--3D Geometry--Horizontal Cross-Section of a Cylinder--Spanish Audio

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Cylinders
Video Definition 56--3D Geometry--Vertical Cross-Sections of a Cylinder Video Definition 56--3D Geometry--Vertical Cross-Sections of a Cylinder Vertical Cross-Sections of a Cylinder

Topic

3D Geometry

Definition

Vertical cross-sections of a cylinder are the intersections of the cylinder with vertical planes, resulting in rectangles or ellipses.

Cylinders
Video Definition 56--3D Geometry--Vertical Cross-Sections of a Cylinder--Spanish Audio Video Definition 56--3D Geometry--Vertical Cross-Sections of a Cylinder--Spanish Audio Video Definition 56--3D Geometry--Vertical Cross-Sections of a Cylinder--Spanish Audio

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Cylinders
Video Definition 9--3D Geometry--Cylinder Video Definition 9--3D Geometry--Cylinder Cylinder

Topic

3D Geometry

Definition

A cylinder is a three-dimensional geometric shape with two parallel circular bases connected by a curved surface.

Description

Cylinders are common in everyday objects, such as cans and pipes. In mathematics, cylinders are studied for their properties, including surface area and volume. The volume V of a cylinder is given by the formula 

V = πr2h

Cylinders
Video Definition 9--3D Geometry--Cylinder--Spanish Audio Video Definition 9--3D Geometry--Cylinder--Spanish Audio Video Definition 9--3D Geometry--Cylinder--Spanish Audio

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Cylinders
Video Transcript: Geometry Applications: 3D Geometry Video Transcript: Geometry Applications: 3D Geometry Video Transcript: Geometry Applications: 3D Geometry

This is the transcript for the video of same title. Video contents: 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.

3-Dimensional Figures and Applications of 3D Geometry
Video Transcript: Geometry Applications: 3D Geometry, Segment 1: Introduction Video Transcript: Geometry Applications: 3D Geometry, Segment 1: Introduction Video Transcript: Geometry Applications: 3D Geometry, Segment 1: Introduction

This is the transcript for the video of same title. Video contents: We visit ancient Greece to learn about the Platonic Solids. This provides an introduction to the more general topic of three-dimensional figures.

This is part of a collection of video transcript from the Geometry Applications video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

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

This is the transcript for the video of same title. Video contents: 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.

3-Dimensional Figures and Applications of 3D Geometry
Video Transcript: Geometry Applications: 3D Geometry, Segment 3: Cylinders Video Transcript: Geometry Applications: 3D Geometry, Segment 3: Cylinders Video Transcript: Geometry Applications: 3D Geometry, Segment 3: Cylinders

This is the transcript for the video of same title. Video contents: 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.

3-Dimensional Figures and Applications of 3D Geometry
VIDEO: 3D Geometry Animation: Antiprism Folding Out into Two Pyramids VIDEO: 3D Geometry Animation: Antiprisms 2 VIDEO: 3D Geometry Animation: Antiprism Folding Out into Two Pyramids

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: Geometry Applications: 3D Geometry VIDEO: Geometry Applications: 3D Geometry VIDEO: Geometry Applications: 3D Geometry

Topic

3D Geometry

3-Dimensional Figures and Applications of 3D Geometry
VIDEO: Geometry Applications: 3D Geometry, Segment 1: Introduction. VIDEO: Geometry Applications: 3D Geometry, 1 VIDEO: Geometry Applications: 3D Geometry, 1

Topic

3D Geometry

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.

This video offers a comprehensive look at the mathematical concepts behind 3D Geometry. Students will gain insights into practical applications and theoretical understanding of the topic, enhancing their ability to visualize and apply these concepts.

3-Dimensional Figures and Applications of 3D Geometry
VIDEO: Geometry Applications: 3D Geometry, Segment 2: Pyramids VIDEO: Geometry Applications: 3D Geometry, 2 VIDEO: Geometry Applications: 3D Geometry, 2

Topic

3D Geometry

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.

This video offers a comprehensive look at the mathematical concepts behind 3D Geometry. Students will gain insights into practical applications and theoretical understanding of the topic, enhancing their ability to visualize and apply these concepts.

3-Dimensional Figures, Pyramids and Applications of 3D Geometry
VIDEO: Geometry Applications: 3D Geometry, Segment 3: Cylinders VIDEO: Geometry Applications: 3D Geometry, 3 VIDEO: Geometry Applications: 3D Geometry, 3

Topic

3D Geometry

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.

This video offers a comprehensive look at the mathematical concepts behind 3D Geometry. Students will gain insights into practical applications and theoretical understanding of the topic, enhancing their ability to visualize and apply these concepts.

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