Surface Area to Volume Ratio Scales Inversely with Side Length

Steps:

• For a cube with side length $s$, surface area is $6s^2$ and volume is $s^3$, so ratio is $6s^2 / s^3 = 6/s$.
• Doubling the side length gives new side $2s$.
• New surface area is $6(2s)^2 = 24s^2$; new volume is $(2s)^3 = 8s^3$.
• New ratio is $24s^2 / 8s^3 = 3/s$, which is half of $6/s$.

Why B is correct:

• The ratio is inversely proportional to side length (from $6/s$); doubling $s$ halves the ratio, per the scaling formula.

Why the others are wrong:

• A: Decreases by a quarter implies new ratio is $3/4$ of original, but it becomes $1/2$.
• C: Ratio decreases, does not double.
• D: Ratio decreases, does not increase by a factor of four.

Final answer: B