Nested Cuboids Problem: Finding Volume Ratio with AC = 1/4 AD

To solve this problem, the approach involves determining the volume of each cuboid and assessing how many times the volume of the small cuboid fits into the volume of the large cuboid.

Step-by-step solution:

• First, note the relationships: $AB = DF$, $BE = FG$, and $AC = \frac{1}{4} AD$. These indicate equivalent heights and widths but differing lengths.
• The sides of the larger cuboid can be assumed as follows for simplification: If $AD = 4x$, then $AC = x$. Since $AB = DF$ and $BE = FG$, widths and heights remain the same for both cuboids.
• The volume of the larger cuboid can be given as: $V_{\text{large}} = (4x) \times w \times h$.
• The volume of the smaller cuboid can be given as: $V_{\text{small}} = x \times w \times h$.
• The ratio of volumes then is $\frac{V_{\text{large}}}{V_{\text{small}}} = \frac{(4x) \times w \times h}{x \times w \times h} = 4$.

Therefore, the smaller cuboid can fit into the larger cuboid 4 times.

The correct answer is 4.