Problem 1. A wooden rectangular prism with edge lengths as natural numbers has a volume of $250 \mathrm{~cm}^{2}$. With one cut, it is divided into two equal cubes. What is the surface area of the rectangular prism?
Solution. Each of the cubes has a volume of $250: 2=125 \mathrm{~cm}^{3}$. If a is the edge of the cube, then $a^{3}=125$, i.e., $a=5 \mathrm{~cm}$. Therefore, the edges of the cuboid are $a, a, 2 a$, i.e., $5 \mathrm{~cm}, 5 \mathrm{~cm}, 10 \mathrm{~cm}$, and its surface area is $P=2(5 \cdot 5+5 \cdot 10+5 \cdot 10) \mathrm{~cm}^{2}=250 \mathrm{~cm}^{2}$.