Volume
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Common Core Standard: Determine the volume of a right rectangular prism with fractional edge lengths by packing
it with unit cubes of 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 = lwh and V = bh to determine the volume
of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical
problems.
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Volume – is the amount of space a three dimensional figure takes up on the inside
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This means that you cannot determine the volume of a rectangle
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But you can determine the volume of a rectangular prism
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Another way to think of volume is by imagining cube units or small cubes filling the space of the figure
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Common Three-Dimensional Figure Vocabulary:
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Face – is the side of a three-dimensional figure
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Congruent – two or more figures, lines, faces, etc. that have the same measure
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Prism – has 2 parallel and congruent faces
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Base – the 2 parallel and congruent faces of a prism are called the base, the shape of the base gives the
figure its name
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The base of a rectangular prism is a rectangle
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The base of a triangular prism is a triangle
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The base cylinder is a circle
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Edge – is the line along two faces
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Vertex – is the spot where two edges meet (the corner)
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This is a square base pyramid, because the base of the pyramid is a square
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Formula:
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The most common shape that you will need to determine the volume of in 6th grade is a rectangular prism
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The formula for the volume of a rectangular prism is length multiplied by width multiplied by height
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V=l•w•h
To determine the length, width, and height use the lengths of the edges of the figure
Example: Determine the volume of a rectangular prism below:
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1st: Determine the shape of the figure, this is a rectangular prism, because the bases are rectangles
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2nd: Determine the appropriate formula or determine if you can use unit cubes (for this example, we will
use the formual): length multiplied by width multiplied by height
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The length of this figure is 30 cm
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The width is 24 cm
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The height is 8 cm
3rd: Determine the volume by using the formula
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30 cm • 24 cm • 8 cm = 5,760 cm3
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Note: The reason the units are cubed, are because when you determined the volume, you
multiplied 30 cm by 24 cm by 8 cm, so really you are multiplying cm by cm by cm, you have three
cm
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Real World Example:
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Kenneth bought an old trunk to store his collection from his travels. The trunk has no shelves. It is the
shape of a rectangular prism. The dimensions of the trunk are 47 ½ in by 22 in by 16 in. Determine the
volume of Kenneth’s trunk.
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1st: This is a rectangular prism
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2nd: The formula is V= l • w • h
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l = 47 ½ in
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w = 22 in
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h = 16 in
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3rd: 47 ½ in • 22 in 16 in = 17, 226 in