1. **Problem:** The surface area of a cube is 54 cm². Find the volume of the cube. 2. **Formula and rules:** - Surface area of a cube: $S = 6a^2$ where $a$ is the side length. - Volume of a cube: $V = a^3$. 3. **Step 1:** Find the side length $a$ from the surface area. $$6a^2 = 54$$ $$a^2 = \frac{54}{6} = 9$$ $$a = \sqrt{9} = 3 \text{ cm}$$ 4. **Step 2:** Calculate the volume using $a=3$ cm. $$V = a^3 = 3^3 = 27 \text{ cm}^3$$ 5. **Answer:** The volume of the cube is $27$ cm³.