## Task 1 - 280731

The volume of a cube $w_{1}$ is eight times as large as the volume of a cube $w_{2}$.

If the volume of $w_{2}$ were exactly $9 \mathrm{~cm}^{3}$ smaller, it would be equal to one twelfth of the volume of $w_{1}$.

Determine from these data the edge lengths $a_{1}$ and $a_{2}$ of the two cubes $w_{1}$ and $w_{2}$!
According to the given information, for the volumes $a_{1}^{3}$ and $a_{2}^{3}$ of $w_{1}$ and $w_{2}$ respectively,

$$
a_{1}^{3}=8 a_{2}^{3} \quad(1) \quad ; \quad a_{2}^{3}-9 \text{ cm}^{3}=\frac{a_{1}^{3}}{12}
$$

From (2) it follows that $12 a_{2}^{3}-108 \text{ cm}^{3}=a_{1}^{3}$, and from this and (1) it follows that

$$
12 a_{2}^{3}-108 \text{ cm}^{3}=8 a_{2}^{3} \quad \Rightarrow \quad a_{2}=3 \text{ cm}
$$

From this and (1), it follows that $a_{1}^{3}=8 \cdot 27 \text{ cm}^{3}, a_{1}=6 \text{ cm}$. (4)

With (3) and (4), the desired edge lengths are determined.