Question

Show that, as the side of a cube decreases by a factor of 10, the surface area

to volume ratio increases by a factor of 10. If on cubes surface area to volume ration is 3 and another cubes surface area to volume ratio is 0.3

Answer 1

As the side of a cube decreases, the surface area to volume ratio increases. For the given cubes, the ratios increase by a factor of 10.

Step-by-step explanation:

When the side of a cube decreases by a factor of 10, its surface area decreases by a factor of 100 (10^2) and its volume decreases by a factor of 1000 (10³). To find the surface area to volume ratio, divide the surface area by the volume.

For the first cube, the surface area to volume ratio is 3. When the side decreases from 3 cm to 0.3 cm, the new surface area to volume ratio will be:

(6 cm²)/(0.027 cm³) = 222.22

Similarly, for the second cube with a surface area to volume ratio of 0.3, when the side decreases from 27 cm to 2.7 cm, the new surface area to volume ratio will be:

(54 cm²)/(0.0729 cm³) = 741.94