# Problem No. 6 (10 points)

The density of a body is defined as the ratio of its mass to the volume it occupies. A homogeneous cube with a volume of \( V = 8 \, \text{m}^3 \) is given. As a result of heating, each of its edges increased by 4 mm. By what percentage did the density of this cube change?

Answer: decreased by \( 6 \% \)
# Solution and evaluation criteria:

Volume of the cube: $v=a^{3}$, where $a$ is the length of the edge, therefore:

$a=2 \partial m=200 mm$.

Final edge length: $a_{\kappa}=204$ mm.

Thus, the final volume: $V_{\kappa}=a_{K}^{3}=2.04^{3}=8.489664 \partial \mu^{3} \approx 1.06 V$.

Therefore, the density:

$\rho_{K}=\frac{m}{V_{K}}=\frac{m}{1.06 V}=0.94 \frac{m}{V} \approx 0.94 \rho$. The density has decreased by approximately $6 \%$.