Illustrative Math Alignment: Grade 6 Unit 1

Dividing Fractions

Lesson 15: Volume of Prisms

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Nodes
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 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 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 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 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 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 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 Topic Volume	Volume
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 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 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 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 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 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 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 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 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
Definition--3D Geometry Concepts--Volume	Volume Topic 3D Geometry Definition Volume is the measure of the amount of space occupied by a three-dimensional object, expressed in cubic units. Description Volume is a fundamental concept in the study of three-dimensional geometry. It quantifies the capacity of a 3D object, indicating how much space it occupies. This measurement is crucial in various fields, including mathematics, engineering, architecture, and physical sciences.	Volume
Definition--3D Geometry Concepts--Volume	Volume Topic 3D Geometry Definition Volume is the measure of the amount of space occupied by a three-dimensional object, expressed in cubic units. Description Volume is a fundamental concept in the study of three-dimensional geometry. It quantifies the capacity of a 3D object, indicating how much space it occupies. This measurement is crucial in various fields, including mathematics, engineering, architecture, and physical sciences.	Volume
Definition--3D Geometry Concepts--Volume	Volume Topic 3D Geometry Definition Volume is the measure of the amount of space occupied by a three-dimensional object, expressed in cubic units. Description Volume is a fundamental concept in the study of three-dimensional geometry. It quantifies the capacity of a 3D object, indicating how much space it occupies. This measurement is crucial in various fields, including mathematics, engineering, architecture, and physical sciences.	Volume
Definition--3D Geometry Concepts--Volume	Volume Topic 3D Geometry Definition Volume is the measure of the amount of space occupied by a three-dimensional object, expressed in cubic units. Description Volume is a fundamental concept in the study of three-dimensional geometry. It quantifies the capacity of a 3D object, indicating how much space it occupies. This measurement is crucial in various fields, including mathematics, engineering, architecture, and physical sciences.	Volume
Formulas--Volume of a Cube	Formulas--Volume of a Cube The formula for the Volume of a Cube. 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
Formulas--Volume of a Cube	Formulas--Volume of a Cube The formula for the Volume of a Cube. 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
Formulas--Volume of a Cube	Formulas--Volume of a Cube The formula for the Volume of a Cube. 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
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
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
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
Formulas--Volume of a Rectangular Prism	Formulas--Volume of a Rectangular Prism The formula for the Volume of a Recantular Prism. 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
Formulas--Volume of a Rectangular Prism	Formulas--Volume of a Rectangular Prism The formula for the Volume of a Recantular Prism. 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
Formulas--Volume of a Rectangular Prism	Formulas--Volume of a Rectangular Prism The formula for the Volume of a Recantular Prism. 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
Formulas--Volume of a Sphere	Formulas--Volume of a Sphere The formula for the Volume of a Sphere. 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
Formulas--Volume of a Sphere	Formulas--Volume of a Sphere The formula for the Volume of a Sphere. 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
Formulas--Volume of a Sphere	Formulas--Volume of a Sphere The formula for the Volume of a Sphere. 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
Formulas--Volume of a Square Pyramid	Formulas--Volume of a Square Pyramid The formula for the Volume of a Square Pyramid. 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
Formulas--Volume of a Square Pyramid	Formulas--Volume of a Square Pyramid The formula for the Volume of a Square Pyramid. 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
Formulas--Volume of a Square Pyramid	Formulas--Volume of a Square Pyramid The formula for the Volume of a Square Pyramid. 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
Formulas--Volume of a Triangular Prism	Note: The download is a JPG file. Related Resources To see the complete collection of Formulas, click on this link: https://media4math.com/math-formulas	Volume
Formulas--Volume of a Triangular Prism	Note: The download is a JPG file. Related Resources To see the complete collection of Formulas, click on this link: https://media4math.com/math-formulas	Volume
Formulas--Volume of a Triangular Prism	Note: The download is a JPG file. Related Resources To see the complete collection of Formulas, click on this link: https://media4math.com/math-formulas	Volume
Formulas--Volume of a Triangular Pyramid	Volume of a Triangular Pyramid Watch this video to learn about the volume of a pyramid. (The video transcript is also included.) Your browser does not support the video tag. Video Transcript Pyramids are majestic and a bit mysterious. Arising from deserts and jungles, they are grand in size and sleek in appearance. Mathematically, pyramids also have an air of mystery. Let’s take a closer look. Here is a cube of side s. Its volume couldn’t be more straightforward: s • s •s, or s-cubed. Its name, its shape, its volume are straightforward.	Volume
Formulas--Volume of a Triangular Pyramid	Volume of a Triangular Pyramid Watch this video to learn about the volume of a pyramid. (The video transcript is also included.) Your browser does not support the video tag. Video Transcript Pyramids are majestic and a bit mysterious. Arising from deserts and jungles, they are grand in size and sleek in appearance. Mathematically, pyramids also have an air of mystery. Let’s take a closer look. Here is a cube of side s. Its volume couldn’t be more straightforward: s • s •s, or s-cubed. Its name, its shape, its volume are straightforward.	Volume
Formulas--Volume of a Triangular Pyramid	Volume of a Triangular Pyramid Watch this video to learn about the volume of a pyramid. (The video transcript is also included.) Your browser does not support the video tag. Video Transcript Pyramids are majestic and a bit mysterious. Arising from deserts and jungles, they are grand in size and sleek in appearance. Mathematically, pyramids also have an air of mystery. Let’s take a closer look. Here is a cube of side s. Its volume couldn’t be more straightforward: s • s •s, or s-cubed. Its name, its shape, its volume are straightforward.	Volume
Promethean Flipchart: Geometry Applications: Area And Volume 2	The glass-paneled pyramid at the Louvre Museum in Paris is a tessellation of rhombus-shaped glass panels. Students create a model of the pyramid to calculate the number of panels used to cover the surface area of the pyramid. Note: The download for this resources is the Promethean Flipchart. To access the full video [Geometry Applications: Area and Volume, Segment 2: Surface Area]: https://media4math.com/library/geometry-applications-area-and-volume-segment-2-surface-area This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-geometry-applications-area-and-volume-segment-2-surface-area	Applications of Surface Area and Volume
Promethean Flipchart: Geometry Applications: Area And Volume 2	The glass-paneled pyramid at the Louvre Museum in Paris is a tessellation of rhombus-shaped glass panels. Students create a model of the pyramid to calculate the number of panels used to cover the surface area of the pyramid. Note: The download for this resources is the Promethean Flipchart. To access the full video [Geometry Applications: Area and Volume, Segment 2: Surface Area]: https://media4math.com/library/geometry-applications-area-and-volume-segment-2-surface-area This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-geometry-applications-area-and-volume-segment-2-surface-area	Applications of Surface Area and Volume
Promethean Flipchart: Geometry Applications: Area And Volume 2	The glass-paneled pyramid at the Louvre Museum in Paris is a tessellation of rhombus-shaped glass panels. Students create a model of the pyramid to calculate the number of panels used to cover the surface area of the pyramid. Note: The download for this resources is the Promethean Flipchart. To access the full video [Geometry Applications: Area and Volume, Segment 2: Surface Area]: https://media4math.com/library/geometry-applications-area-and-volume-segment-2-surface-area This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-geometry-applications-area-and-volume-segment-2-surface-area	Applications of Surface Area and Volume
Promethean Flipchart: Geometry Applications: Area And Volume 2	The glass-paneled pyramid at the Louvre Museum in Paris is a tessellation of rhombus-shaped glass panels. Students create a model of the pyramid to calculate the number of panels used to cover the surface area of the pyramid. Note: The download for this resources is the Promethean Flipchart. To access the full video [Geometry Applications: Area and Volume, Segment 2: Surface Area]: https://media4math.com/library/geometry-applications-area-and-volume-segment-2-surface-area This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-geometry-applications-area-and-volume-segment-2-surface-area	Applications of Surface Area and Volume
Promethean Flipchart: Geometry Applications: Area And Volume 2	The glass-paneled pyramid at the Louvre Museum in Paris is a tessellation of rhombus-shaped glass panels. Students create a model of the pyramid to calculate the number of panels used to cover the surface area of the pyramid. Note: The download for this resources is the Promethean Flipchart. To access the full video [Geometry Applications: Area and Volume, Segment 2: Surface Area]: https://media4math.com/library/geometry-applications-area-and-volume-segment-2-surface-area This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-geometry-applications-area-and-volume-segment-2-surface-area	Applications of Surface Area and Volume
Promethean Flipchart: Geometry Applications: Area And Volume 3	The Citibank Tower in New York City presents some unique design challenges. In addition it has to cope with a problem that all tall structure have to deal with: heat loss. By managing the ratio of surface area to volume, a skyscraper can effective manage heat loss. Note: The download for this resources is the Promethean Flipchart. To access the full video [Geometry Applications: Area and Volume, Segment 3: Ratio of Surface Area to Volume]: https://www.media4math.com/library/geometry-applications-area-and-volume-segment-3-ratio-surface-area-volume	Applications of Surface Area and Volume
Promethean Flipchart: Geometry Applications: Area And Volume 3	The Citibank Tower in New York City presents some unique design challenges. In addition it has to cope with a problem that all tall structure have to deal with: heat loss. By managing the ratio of surface area to volume, a skyscraper can effective manage heat loss. Note: The download for this resources is the Promethean Flipchart. To access the full video [Geometry Applications: Area and Volume, Segment 3: Ratio of Surface Area to Volume]: https://www.media4math.com/library/geometry-applications-area-and-volume-segment-3-ratio-surface-area-volume	Applications of Surface Area and Volume
Promethean Flipchart: Geometry Applications: Area And Volume 3	The Citibank Tower in New York City presents some unique design challenges. In addition it has to cope with a problem that all tall structure have to deal with: heat loss. By managing the ratio of surface area to volume, a skyscraper can effective manage heat loss. Note: The download for this resources is the Promethean Flipchart. To access the full video [Geometry Applications: Area and Volume, Segment 3: Ratio of Surface Area to Volume]: https://www.media4math.com/library/geometry-applications-area-and-volume-segment-3-ratio-surface-area-volume	Applications of Surface Area and Volume