Visible Unit Cubes on the Surface of a 10×10×10 Cube
Problem
A \( 10 \times 10 \times 10 \) cube is made up of \( 1000 \) unit cubes. How many of these unit cubes are visible on the outside?
Step 1: Total Number of Cubes
\[ 10 \times 10 \times 10 = 1000 \quad \text{unit cubes} \]
Step 2: Hidden Interior Cubes
The cubes that are not visible are the ones fully inside the cube, not on any face.
These form an interior cube of size:
\[ (10 - 2)^3 = 8^3 = 512 \]
These are the cubes that are not visible from any side.
Step 3: Visible Cubes
The visible unit cubes are all those not fully enclosed, i.e., those not in the 8×8×8 cube:
\[ 1000 - 512 = \boxed{488} \]
Conclusion
There are \( \boxed{488} \) unit cubes visible on the surface of a \( 10 \times 10 \times 10 \) cube.