12) From a piece of wood in the shape of a rectangular parallelepiped, one wants to extract another parallelepiped with dimensions $3 \mathrm{~cm} \times 4 \mathrm{~cm} \times 5 \mathrm{~cm}$ by making three cuts parallel to the faces. When working with the saw, it can only be guaranteed that the actual dimensions will deviate by at most $1 \mathrm{~mm}$ from the desired ones. How much can the volume of the constructed parallelepiped deviate, at most, from that of the desired parallelepiped?
(A) About $0.5 \mathrm{~cm}^{3}$
(E) about $4.8 \mathrm{~cm}^{3}$.
(B) about $1.2 \mathrm{~cm}^{3}$
(C) about $2 \mathrm{~cm}^{3}$
(D) about $2.4 \mathrm{~cm}^{3}$
12) The answer is $(\mathrm{E})$.

The desired volume of the parallelepiped is $3 \times 4 \times 5=60 \mathrm{~cm}^{3}$. The actual volume can vary from a minimum of $2.9 \times 3.9 \times 4.9 \approx 55.4 \mathrm{~cm}^{3}$ to a maximum of $3.1 \times 4.1 \times 5.1 \approx 64.8 \mathrm{~cm}^{3}$.

Note that the maximum deviation is given by the volume of a thickness applied to three faces of the desired parallelepiped with a height of $1 \mathrm{~mm}$, and that this volume is, in the first approximation, the product of half the lateral surface area by the height of $1 \mathrm{~mm}$, which is $4.7 \mathrm{~cm}^{3}$.