8. A cube consists of eight smaller identical cubes. Two of the smaller cubes were replaced with ones of the same size but with a density twice as high. Determine the ratio of the initial and final densities of the large cube. (10 points)
Answer: 0.8

Solution. The relationship between mass and volume: $m=\rho V$ (2 points), that is, the new cubes, with the same volume, are twice as heavy. Initial density: $\rho_{\text {initial }}=\frac{8 m_{0}}{8 V_{0}} \quad$ (3 points).

Final density: $\quad \rho_{\text {final }}=\frac{6 m_{0}+2 m_{1}}{8 V_{0}}=\frac{6 m_{0}+2 \cdot 2 m_{0}}{8 V_{0}}=\frac{10 m_{0}}{8 V_{0}} \quad(3$ points $)$.

Final result: $\frac{\rho_{\text {initial }}}{\rho_{\text {final }}}=\frac{8}{10}=0.8$ (2 points).

## Final Stage

 $2017-2018$ academic year
## Tasks, answers, and evaluation criteria  7th grade  Variant II  h วłf Ћ วłGr ə