Final answer:
The dimensions of a box with a square base, a volume of 343, and minimal surface area are 7x7x7 units, forming a cube.
Step-by-step explanation:
The student is asking how to find the dimensions of a box with a square base that has a given volume and the minimal surface area. Let's denote the side length of the square base as 's' and the height of the box as 'h'. The volume of the box, which is 343 cubic units, is defined by the formula V=s^2*h. To minimize the surface area, we should create a box where s=h, forming a cube. The reason for this is that a cube has the lowest possible surface area for a given volume.
To find the dimensions, we first calculate s by taking the cube root of the volume:
Thus, the side length of the base and the height are both 7 units to form a cube with the minimal surface area and a volume of 343 cubic units.