If each edge of a cube is doubled, then its volume:

### Concept & Volumetric Scaling The volume of a cube depends on the cube of its edge length. When the 1D dimension is scaled by a factor $k$, the 3D volume scales by $k^3$. $$V = a^3$$ ### Step-by-Step Solution 1. **Initial Volume:** - Let the original edge of the cube be $a$. - The original volume is $V_1 = a^3$. 2. **New Volume:** - The edge is doubled, so the new edge is $2a$. - The new volume is $V_2 = (2a)^3$. 3. **Compare Volumes:** - $V_2 = 8 \times a^3$. - Since $a^3 = V_1$, we have $V_2 = 8 \times V_1$. 4. **Conclusion:** - The volume becomes 8 times the original volume. ### Exam Strategy & Shortcut Always remember the dimensional rule: scaling a length by $N$ scales the area by $N^2$ and the volume by $N^3$. If the edge is doubled ($N=2$), the volume increases by $2^3 = 8$ times. ### Common Pitfall Students often confuse volume scaling with length or area scaling and mistakenly answer "is doubled" or "becomes 4 times". ### Final Answer Therefore, the correct answer is **becomes 8 times**.