Math Problem Statement
Robert is filling a box that is a rectangular prism with a height of 1 1/3 meters, a length of 1 meter, and width of 2/3 meters. How many 1/3 meter cubes will Robert need to fill the box?
Solution
To determine how many -meter cubes Robert will need to fill the box, follow these steps:
Step 1: Calculate the volume of the rectangular prism
The volume of a rectangular prism is calculated as: Substituting the given dimensions:
Step 2: Calculate the volume of one -meter cube
The volume of one cube with a side length of meter is:
Step 3: Determine the number of -meter cubes
To find the total number of cubes required, divide the volume of the rectangular prism by the volume of one cube: Perform the division by multiplying by the reciprocal of :
Final Answer:
Robert will need 24 cubes to fill the box.
Would you like a detailed explanation of any step, or do you have further questions?
Here are 5 related questions to expand on this:
- How would the number of cubes change if the box dimensions were doubled?
- What is the total surface area of the rectangular prism?
- How do you calculate the surface area of one -meter cube?
- How many -meter cubes would fit into the same box?
- What is the significance of unit conversions when solving volume problems?
Tip: When working with fractions in geometry problems, always simplify intermediate steps to minimize errors.
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Math Problem Analysis
Mathematical Concepts
Volume of a rectangular prism
Volume of a cube
Division of fractions
Formulas
Volume of rectangular prism = height × length × width
Volume of cube = side³
Number of cubes = Volume of prism ÷ Volume of one cube
Theorems
Principle of volume calculation for composite solids
Reciprocal rule for division of fractions
Suitable Grade Level
Grades 5-7
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