1. The problem states that the volume of a 3D rectangular solid formed by combining two cubes is 1458 cm³, and we need to find the unknown side length $x$ cm. 2. The volume $V$ of a cube with side length $x$ is given by the formula: $$V = x^3$$ 3. Since the solid is formed by combining two cubes, the total volume is: $$2x^3 = 1458$$ 4. To find $x$, solve the equation: $$2x^3 = 1458$$ Divide both sides by 2: $$x^3 = \frac{1458}{2} = 729$$ 5. Now find the cube root of 729: $$x = \sqrt[3]{729}$$ Since $9^3 = 729$, we have: $$x = 9$$ 6. Therefore, the unknown side length $x$ is 9 cm. Final answer: $x = 9$ cm.