8. On a table there are two identical wooden blocks, in the shape of a parallelepiped. Clara wants to stack them one on top of the other, making sure that the two faces in contact are different. By doing so, the total height of the stack can be either $22 \mathrm{~cm}$ or $30 \mathrm{~cm}$ or $32 \mathrm{~cm}$. How many $\mathrm{cm}^{3}$ is the volume of a block?
(A) 2400
(B) 2700
(C) 3000
(D) 2800
(E) 1800
Problem 8. The correct answer is (A).

By adding the three heights of the stacks formed by two pieces, we get $22+30+32=84 \mathrm{~cm}$. In this total, each of the heights has been added twice, so the sum of the three heights is $84 / 2=42 \mathrm{~cm}$. The three heights are therefore (in $\mathrm{cm}$ ) $42-22=20,42-30=12,42-32=10$, which will be the lengths of the three edges of a brick. The volume is thus equal to $20 \cdot 12 \cdot 10=2400 \mathrm{~cm}^{2}$.