Question

A solid object made of cubes is shown. It is symmetric about all three axes, and has no cavities. How many cubes does the solid contain?

Hint:

When counting cubes, split into layers along symmetry planes. Symmetry ensures the same number is repeated across axes.

Answer 1

Step 1: Recognise shape.
The figure is a stepped cube structure, symmetric along x, y, z axes.
Step 2: Cube counting.
- Central solid: $3 \times 3 \times 3 = 27$ cubes.
- Middle layers extend symmetrically, adding $20$ cubes.
- Outer layer contributes another $16$ cubes.
Step 3: Total.
\[ 27 + 20 + 16 = 63 \] Final Answer: \[ \boxed{63 \, \text{cubes}} \]