Answer:
Just less than 3.11
Step-by-step explanation:
Actually, this problem doesn't have a single answer. Rather, you are asked to use estimation and educated guesses to determine the length of one side of the middle cube.
Note that the volume of the first cube is 3^3 = 27, and that the vol. of the third cube is 4^3 = 64. So we can see right away that all sides of the middle cube have a length which is between 3 and 4.
Suppose I picked s = 3.5 out of the blue and then cubed it: 3.5^3 = 42.875 cubic units. Much too big! So try s = 3.25: 3.25^3 = 34.33. Better, but still too big. We want a side length that gives us the volume 30 for this middle cube.
Try 3.2^3: volume is 32.8 (too big)
Try 3.1^3: vol. is 29.8 (too small) Try a value slightly larger than 3.1:
Try 3.12^3: vol. is 30.37 (slightly too large)
Try 3.115^3: vol. is 30.3 (better, but still slightly too large)
Try 3.113^3: vol. is 30.2 (better still, but keep on going!)
You'll find that the correct side length is between 3.113 and 3.106.
