Question

Count the number of cubes in the figure. No cube has been removed from parts that are not visible. 

Hint:

For “count the cubes” visuals, assume solid vertical stacks and sum by horizontal layers from top to bottom. It’s faster and avoids double counting edges you can’t see.

Answer 1

Step 1: Treat the solid as vertical stacks on a square base.
From the isometric view, every visible column of unit cubes sits on the base and rises without gaps (statement says no hidden cubes are removed). So the solid can be counted layer by layer.
Step 2: Count cubes layer-wise.
Reading the terraces from top to bottom and marking each complete layer gives the following counts:
Layer 6: $9$ cubes;
Layer 5: $20$ cubes;
Layer 4: $28$ cubes;
Layer 3: $31$ cubes;
Layer 2: $34$ cubes;
Layer 1 (bottom): $36$ cubes.
Step 3: Total.
\[ 36+34+31+28+20+9 \;=\; \boxed{158}. \]