Math Problem Statement
The volume of Figure 1 is:
Solution
Let's solve the problem based on the uploaded image.
Given Information:
- The figure is composed of cubic blocks.
- The steps form a rectangular prism structure divided into three levels.
- The base dimensions of the figure are , and the height is (split into 3 levels of height 2 each).
Step-by-Step Solution:
-
Determine the size of each cube:
- Since the total height is , divided into levels, the height of one cube is .
- Therefore, each cube is in dimensions.
-
Calculate the total number of cubes:
- Level 1 (bottom level): This level is , so it contains cubes.
- Level 2 (middle level): This level is , so it contains cubes.
- Level 3 (top level): This level is , so it contains cube.
- Total number of cubes = .
-
Calculate the volume of each cube:
- The volume of one cube = .
-
Calculate the total volume:
- Total volume = .
Final Answer:
Since is not one of the options, the correct answer is "none of these."
Would you like further clarification or have any questions?
Here are 5 follow-up questions for further understanding:
- What is the formula for calculating the volume of a cube or rectangular prism?
- How do we determine the dimensions of a single unit block from the overall structure?
- Why is it important to carefully count the blocks at each level of the structure?
- How would the volume change if the cubes were of size ?
- How can we verify the calculations using an alternative method?
Tip:
When dealing with 3D structures, always break the figure into smaller, simpler components for easy calculations!
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Math Problem Analysis
Mathematical Concepts
Mensuration
Volume of solids
Counting cubic blocks
Formulas
Volume of a cube = side^3
Total volume = sum of volumes of all cubes
Theorems
Volume computation in 3D structures
Suitable Grade Level
Grades 6-8