Podcast
Questions and Answers
A container is filled with identical small cubes. If determining the container's volume reveals the total number of cubes it can hold, what concept does this best illustrate?
A container is filled with identical small cubes. If determining the container's volume reveals the total number of cubes it can hold, what concept does this best illustrate?
- Density—the relationship between the cube's mass and how tightly they fit within the container.
- The additive property of volume, where the volume of the container is approximately the sum of the volumes of the individual cubes.
- Surface area, as volume only considers the outer faces of the container and cubes.
- Volume as the amount of space a three-dimensional object occupies, which can be quantified by the number of unit cubes it holds. (correct)
If a cube has sides of length 4 units, and the formula for volume is $V=s^3$, what is the volume of the cube?
If a cube has sides of length 4 units, and the formula for volume is $V=s^3$, what is the volume of the cube?
- 81 cubic units
- 12 cubic units
- 16 cubic units
- 64 cubic units (correct)
An object's dimensions are tripled. How does this affect its volume, assuming it is a cube?
An object's dimensions are tripled. How does this affect its volume, assuming it is a cube?
- The volume increases by a factor of 27. (correct)
- The volume increases by a factor of 3.
- The volume increases by a factor of 9.
- The volume remains the same because the shape is unchanged.
A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Which calculation correctly determines its volume?
A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Which calculation correctly determines its volume?
A cube has a volume of 64 cubic inches. What is the length of one side of the cube?
A cube has a volume of 64 cubic inches. What is the length of one side of the cube?
Flashcards
What is volume?
What is volume?
The amount of space occupied by a three-dimensional object or substance.
What is a cube?
What is a cube?
A 3D shape with six square faces, all sides being equal.
What is a rectangular prism?
What is a rectangular prism?
A 3D shape with six rectangular faces.
Volume of a cube formula
Volume of a cube formula
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What is a 3D Solid?
What is a 3D Solid?
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Study Notes
- A Rubik's cube is a three-dimensional solid figure.
- The dimensions of a Rubik's cube are length, width, and height.
- A Rubik's cube has 27 small cubes.
- Finding the total number of cubes on a container determines its volume.
- Volume is the amount of space occupied by a quantity.
- The topic is visualizing the volume of a cube and rectangular prism.
- Volume of a cube is found using the formula V = s x s x s or V = s³.
- Example 1:
- V = s³
- V = 3 x 3 x 3 or s³
- V = 9 x 3
- V = 27
- Example 2:
- V = s³
- V = s x s x s
- V = 5 x 5 x 5
- V = 25 x 5
- V = 125
- A rectangular prism is discussed after the volume of a cube.
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Description
Learn how to find the volume of a cube by visualizing it as a three-dimensional figure. We use the formula V = s x s x s or V = s³ to calculate the volume. The lesson furthers explains the volume of a rectangular prism.
