Question

what happens to the volume and surface area when dividing a cube into smaller pieces (with explanation)​

Answer 1

The total volume is the same and the total surface area doubles.

Step-by-step explanation:

We know that the total volume for the large cube and the total volume for the small cubes is the same but that the surface area for the smaller cubes is double that of the large cube. So the volume-to-surface-area ratio is as to for the large cube and as to two for the small cubes. The smaller cubes are much more reactive than the large cube because of this ratio. And that is why nanoparticles are so reactive and so useful to us because of this large surface area and very small particles.

Answer 2

Answer: Upon successive breakage into smaller cubes, each time by halving the sides, the volume remains constant while the surface area increases dramatically. The total area of all cubes at each iteration is the red dot on the continuous line plot of area/volume.

Explanation: Hope this helps