Question

Count the number of cubes in the following geometrically symmetric regular solid.

Hint:

When counting cubes in a 3D arrangement, use the formula for the volume of a cube and apply it to the number of smaller cubes stacked together.

Answer 1

Step 1: Understanding the Solid.
The solid shown is a 3D arrangement of cubes, forming a larger geometric structure. The image suggests a symmetric arrangement of smaller cubes stacked in a regular formation.
Step 2: Breaking the Structure into Layers.
Upon examining the structure, we observe that it is formed by smaller cubes, each with a side length of 1 unit, arranged in a 3x3x3 formation.
Step 3: Counting the Cubes.
The total number of small cubes in a 3D arrangement with dimensions 3x3x3 can be calculated as: \[ \text{Total number of cubes} = 3^3 = 27. \] Therefore, the number of cubes in the structure is \( 27 \).
Step 4: Conclusion.
Thus, the total number of cubes in the given solid is \( 27 \).
\[ \boxed{27} \]