Math Problem Statement
solve it
Solution
The image shows a rectangular prism made of unit cubes, with the base dimensions of 1 meter and cubes arranged in a grid.
To find the volume of the rectangular prism, we need to calculate the number of unit cubes that make up the entire structure. Each cube represents 1 cubic meter (m³).
The rectangular prism has:
- Length: 4 cubes (each cube is 1 meter, so total length is 4 meters),
- Width: 2 cubes (total width is 2 meters),
- Height: 2 cubes (total height is 2 meters).
The formula for the volume of a rectangular prism is:
Substituting the values:
Thus, the volume of the rectangular prism is .
Do you want more details or have any questions?
Here are 5 related questions to expand on this:
- How would the volume change if the height were doubled?
- What is the surface area of this rectangular prism?
- How does the volume change if each dimension is increased by 50%?
- What is the formula for the volume of a cube and how does it compare to the prism's volume formula?
- If the unit cubes had a different size, how would that affect the total volume?
Tip: The volume of any solid object can be found by multiplying its dimensions (length, width, height). Always make sure the units are consistent!
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Math Problem Analysis
Mathematical Concepts
Geometry
Volume Calculation
Rectangular Prism
Formulas
Volume of a rectangular prism: V = length × width × height
Theorems
Basic volume calculation theorem for prisms
Suitable Grade Level
Grades 5-7