4. Is it enough to make a closed rectangular box from all sides, enclosing no less than 1995 unit cubes, a) 962; b) 960; c) 958 square units of material?
4. It is sufficient to take a box of size $11 \times 13 \times 14$. Its volume is 2002, which is sufficient; and the total area of its walls is $2 \cdot(11 \cdot 13+11 \cdot 14+13 \cdot 14)=958$.

Comments. $1^{\circ}$. How can one guess such a solution? It is known that among all parallelepipeds with a given volume, the cube has the minimum surface area - this follows from the inequality between the arithmetic mean and the geometric mean, see fact 26. However, a cube with a volume of 1995 would have irrational side lengths. Therefore, one needs to try to find a box that is close in shape to a cube but with integer side lengths. The "nearest" cubes are $12 \times 12 \times 12$ and $13 \times 13 \times 13$ (their volumes are 1728 and 2197, respectively). It might seem that the most "economical" option is $12 \times 13 \times 13$. Unfortunately, this parallelepiped only provides a solution for part "a". Continuing to search for parallelepipeds close to a cube, one can find the solution to the problem.

$2^{\circ}$. 957 units of material are not enough to make the box.