6.G.2: Find the volume of a right rectangular prism with...

# Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Cube-shaped boxes will be loaded into the cargo hold of a truck.
The cargo hold of the truck is in the shape of a rectangular prism. The edges of each box measure 2.50 feet and the dimensions of the cargo hold are 7.50 feet by 15.00 feet by 7.50 feet, as shown below.

What is the volume, in cubic feet, of each box?
Determine the number of boxes that will completely fill the cargo hold of the truck. Use words and/or numbers to show how you determined your answer.
Cube-shaped boxes will be loaded into the cargo hold of a truck.
The cargo hold of the truck is in the shape of a rectangular prism. The edges of each box measure 2.50 feet and the dimensions of the cargo hold are 7.50 feet by 15.00 feet by 7.50 feet, as shown below.

What is the volume, in cubic feet, of each box?
Determine the number of boxes that will completely fill the cargo hold of the truck. Use words and/or numbers to show how you determined your answer.
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Emma Stone is managing a storage business. She has a small unit available with the dimensions of the figure below. Each standard box is $$\frac{1}{2}$$ m. on each side. How many boxes will fit in the available space? What is the total volume of the space?

Emma Stone is managing a storage business. She has a small unit available with the dimensions of the figure below. Each standard box is $$\frac{1}{2}$$ m. on each side. How many boxes will fit in the available space? What is the total volume of the space?
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Jennifer Lawrence made rice crispy treats in a 9 x 13 x 2$$\frac{1}{2}$$ inch cake pan.
(a) How many $$\frac{1}{2}$$ in. x $$\frac{1}{2}$$ in. rice crispy treats could be cut from the pan?
(b) What is the total volume of rice crispy treats?
Jennifer Lawrence made rice crispy treats in a 9 x 13 x 2$$\frac{1}{2}$$ inch cake pan.
(a) How many $$\frac{1}{2}$$ in. x $$\frac{1}{2}$$ in. rice crispy treats could be cut from the pan?
(b) What is the total volume of rice crispy treats?

A right rectangular prism has edge lengths 1$$\frac{1}{3}$$", 2", and 1$$\frac{2}{3}$$". How many cubes with edge lengths $$\frac{1}{3}$$" would be needed to fill the prism? What is the volume of the prism?
A right rectangular prism has edge lengths 1$$\frac{1}{3}$$", 2", and 1$$\frac{2}{3}$$". How many cubes with edge lengths $$\frac{1}{3}$$" would be needed to fill the prism? What is the volume of the prism?
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Christo and Jeanne Claude are artists who wrap large things – bridges, buildings, even islands. (See www.christojeanneclaude.net for images.)
Imagine that Jean Claude and Christo are preparing for their next large project – that of wrapping a large building. They are building a scale model in order to plan out the project.
The model building will measure 11$$\frac{1}{2}$$ inches high, and 7$$\frac{1}{2}$$ inches wide, and 6 inches long.
They are considering building the model with blocks that measure $$\frac{1}{2}$$ in. on each side.
(a) What is the volume of the building in cubic inches?
(b) How many of the blocks that measure $$\frac{1}{2}$$ in. on each side would Jeanne Claude and Christo need to make the model building?
(c) Draw a picture of the model building and determine how much fabric Jean Claude and Christo will need to cover the model building.
(d) The way Jean Claude and Christo have made their model, they know that the number of square feet needed to cover the real building is 144 times the number of square inches needed to cover the model. How much fabric will Jean Claude and Christo need to cover the real building?
Christo and Jeanne Claude are artists who wrap large things – bridges, buildings, even islands. (See www.christojeanneclaude.net for images.)
Imagine that Jean Claude and Christo are preparing for their next large project – that of wrapping a large building. They are building a scale model in order to plan out the project.
The model building will measure 11$$\frac{1}{2}$$ inches high, and 7$$\frac{1}{2}$$ inches wide, and 6 inches long.
They are considering building the model with blocks that measure $$\frac{1}{2}$$ in. on each side.
(a) What is the volume of the building in cubic inches?
(b) How many of the blocks that measure $$\frac{1}{2}$$ in. on each side would Jeanne Claude and Christo need to make the model building?
(c) Draw a picture of the model building and determine how much fabric Jean Claude and Christo will need to cover the model building.
(d) The way Jean Claude and Christo have made their model, they know that the number of square feet needed to cover the real building is 144 times the number of square inches needed to cover the model. How much fabric will Jean Claude and Christo need to cover the real building?
Volume of right rectangular prisms with fractional edge lengths - unit cubes

The pool at the London Aquatics Center has the dimensions of the figure below. The pool is drained and refilled every night. What volume of water would be required to fill the pool to the rim?

The pool at the London Aquatics Center has the dimensions of the figure below. The pool is drained and refilled every night. What volume of water would be required to fill the pool to the rim?

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Andrew Luck is designing an office building with the dimensions of the figure below. Before he orders the air conditioning system, he needs to know the total volume of air that needs to be cooled. What is the total volume of the office building?

Andrew Luck is designing an office building with the dimensions of the figure below. Before he orders the air conditioning system, he needs to know the total volume of air that needs to be cooled. What is the total volume of the office building?

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Christo and Jeanne Claude are artists who wrap large things – bridges, buildings, even islands. (See www.christojeanneclaude.net for images.)
Imagine that Jean Claude and Christo are preparing for their next large project – that of wrapping a large building. They are building a scale model in order to plan out the project.
The model building will measure 11$$\frac{1}{2}$$ inches high, and 7$$\frac{1}{2}$$ inches wide, and 6 inches long.
They are considering building the model with blocks that measure $$\frac{1}{2}$$ in. on each side.
(a) What is the volume of the building in cubic inches?
(b) How many of the blocks that measure $$\frac{1}{2}$$ in. on each side would Jeanne Claude and Christo need to make the model building?
(c) Draw a picture of the model building and determine how much fabric Jean Claude and Christo will need to cover the model building.
(d) The way Jean Claude and Christo have made their model, they know that the number of square feet needed to cover the real building is 144 times the number of square inches needed to cover the model. How much fabric will Jean Claude and Christo need to cover the real building?
Christo and Jeanne Claude are artists who wrap large things – bridges, buildings, even islands. (See www.christojeanneclaude.net for images.)
Imagine that Jean Claude and Christo are preparing for their next large project – that of wrapping a large building. They are building a scale model in order to plan out the project.
The model building will measure 11$$\frac{1}{2}$$ inches high, and 7$$\frac{1}{2}$$ inches wide, and 6 inches long.
They are considering building the model with blocks that measure $$\frac{1}{2}$$ in. on each side.
(a) What is the volume of the building in cubic inches?
(b) How many of the blocks that measure $$\frac{1}{2}$$ in. on each side would Jeanne Claude and Christo need to make the model building?
(c) Draw a picture of the model building and determine how much fabric Jean Claude and Christo will need to cover the model building.
(d) The way Jean Claude and Christo have made their model, they know that the number of square feet needed to cover the real building is 144 times the number of square inches needed to cover the model. How much fabric will Jean Claude and Christo need to cover the real building?

Leo's recipe for banana bread won't fit in his favorite pan. The batter fills the 8.5 inch by 11 inch by 1.75 inch pan to the very top, but when it bakes it spills over the side. He has another pan that is 9 inches by 9 inches by 3 inches, and from past experience he thinks he needs about an inch between the top of the batter and the rim of the pan. Should he use this pan?
Leo's recipe for banana bread won't fit in his favorite pan. The batter fills the 8.5 inch by 11 inch by 1.75 inch pan to the very top, but when it bakes it spills over the side. He has another pan that is 9 inches by 9 inches by 3 inches, and from past experience he thinks he needs about an inch between the top of the batter and the rim of the pan. Should he use this pan?
Volume of right rectangular prisms with fractional edge lengths - formula

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