What is the maximum number of identical pieces a cube can be cut into by 3 cuts?a.6b.12c.4d.8

Break Down the Problem

1. Identify the question: We need to determine the maximum number of identical pieces a cube can be divided into with 3 cuts.

Relevant Concepts

2. Understand how cuts in three-dimensional objects work:
   • A single cut can divide an object into two pieces.
   • Each subsequent cut can potentially intersect all previous cuts.

Analysis and Detail

3. Consider the cuts:
   • First Cut: Dividing the cube into 2 pieces.
   • Second Cut: If placed strategically, this cut can go through both pieces created from the first cut and divide them further. This can lead to a maximum of 4 pieces.
   • Third Cut: By strategically positioning this cut to intersect the existing pieces created from the first and second cuts, it can potentially double the number of pieces again.

To visualize:

• After the first cut: 2 pieces.
• After the second cut: 4 pieces (if cut through both).
• After the third cut: 8 pieces (cutting through all 4 pieces).

Verify and Summarize

4. Therefore, after applying the theory of maximum cuts in three dimensions, we can confirm that 3 cuts can yield a maximum of 8 pieces. The cuts must be made strategically to ensure they intersect all existing sections.

Final Answer

The maximum number of identical pieces a cube can be cut into by 3 cuts is 8 (Option d).