Consider the ratio of the surface area of a cube to its volume. What happens to this ratio if the side length of the cube decreases by a factor of 2?
A) Increases by a factor of 4
B) Decreases by a factor of 4
C) Increases by a factor of 2
D) Decreases by a factor of 2
E) Remains the same

Question

Quizplus · Accepted Answer

The surface area of a cube is given by $6a^2$ and its volume by $a^3$, where $a$ is the side length. The ratio of surface area to volume is $\frac{6a^2}{a^3} = \frac{6}{a}$. If the side length decreases by a factor of 2, $a$ becomes $\frac{a}{2}$, making the new ratio $\frac{6}{a/2} = \frac{12}{a}$, which is an increase by a factor of 2.

Consider the Ratio of the Surface Area of a Cube