Two cubes have edge lengths $2$ and $4$. What is the ratio of their **…

Question

Two cubes have edge lengths $2$ and $4$. What is the ratio of their **volumes** (smaller : larger)?

Accepted Answer

B. $1 : 8$

Volume scales as the **cube** of the linear scale factor. Edge ratio $2 : 4 = 1 : 2$. Volume ratio $= 1^{3} : 2^{3} = 1 : 8$.
Direct: $V_{1} = 8$, $V_{2} = 64$, ratio $= 8 : 64 = 1 : 8$ ✓.
- Trap A returns the edge ratio.
- Trap B returns the **surface area** ratio.
- Trap D returns $1 : 4^{2}$.

Answer

$1 : 2$

Answer

$1 : 16$

Answer

$1 : 4$