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 3×33 \times 3, and the height is 66 (split into 3 levels of height 2 each).

Step-by-Step Solution:

  1. Determine the size of each cube:

    • Since the total height is 66, divided into 33 levels, the height of one cube is 22.
    • Therefore, each cube is 2×2×22 \times 2 \times 2 in dimensions.
  2. Calculate the total number of cubes:

    • Level 1 (bottom level): This level is 3×33 \times 3, so it contains 99 cubes.
    • Level 2 (middle level): This level is 2×22 \times 2, so it contains 44 cubes.
    • Level 3 (top level): This level is 1×11 \times 1, so it contains 11 cube.
    • Total number of cubes = 9+4+1=149 + 4 + 1 = 14.
  3. Calculate the volume of each cube:

    • The volume of one cube = 23=8units32^3 = 8 \, \text{units}^3.
  4. Calculate the total volume:

    • Total volume = 14×8=112units314 \times 8 = 112 \, \text{units}^3.

Final Answer:

Since 112112 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:

  1. What is the formula for calculating the volume of a cube or rectangular prism?
  2. How do we determine the dimensions of a single unit block from the overall structure?
  3. Why is it important to carefully count the blocks at each level of the structure?
  4. How would the volume change if the cubes were of size 1×1×11 \times 1 \times 1?
  5. 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