11.073. The measurements of a rectangular parallelepiped are 2, 3, and 6 cm. Find the length of the edge of a cube such that the volumes of these bodies are in the same ratio as their surface areas.
Solution.

The volume of a rectangular parallelepiped is $V_{\text {par }}=2 \cdot 3 \cdot 6=36 \mathrm{~cm}^{3}$. The volume of a cube is $V_{\mathrm{x}}=a^{3}$. The area of the complete surface of a rectangular parallelepiped is calculated as follows: $S_{\text {par }}=S_{\text {side }}+2 S_{\text {base }}=P H+2 S_{\text {base }}=2(2+3) \cdot 6+$ $+2 \cdot 3 \cdot 2=72 \mathrm{~cm}^{2}$. The area of the complete surface of a cube is $S_{\mathrm{K}}=6 a^{2}$. From the condition $\frac{V_{\text {par }}}{V_{\mathrm{K}}}=\frac{S_{\text {par }}}{S_{\mathrm{K}}}$. Hence, $\frac{36}{a^{3}}=\frac{72}{6 a^{2}}$. We get $a=3$ cm.

Answer: 3 cm.