1. **Problem:** Three metallic cubes with edges 3 cm, 4 cm, and 5 cm are melted to form a single cube. Find the edge length and surface area of the new cube. 2. **Formula:** Volume of cube = $a^3$ where $a$ is edge length. 3. **Step 1:** Calculate volumes of individual cubes: - Volume$_1$ = $3^3 = 27$ cm³ - Volume$_2$ = $4^3 = 64$ cm³ - Volume$_3$ = $5^3 = 125$ cm³ 4. **Step 2:** Total volume = $27 + 64 + 125 = 216$ cm³ 5. **Step 3:** Let edge of new cube be $x$. Then $x^3 = 216$. 6. **Step 4:** Solve for $x$: $$x = \sqrt[3]{216} = 6 \text{ cm}$$ 7. **Step 5:** Surface area of cube = $6x^2 = 6 \times 6^2 = 6 \times 36 = 216$ cm² **Final answer:** Edge length = 6 cm, Surface area = 216 cm²