If a metal slab of size 1 m $\times$ 20 cm $\times$ 1 cm is melted to another slab of 1 mm thickness and 1 m width, then the length of the new slab thus formed will be

### Concept & Conservation of Volume When a solid is melted and recast into a new shape, the total volume of material remains constant. $$ V_{\text{old}} = V_{\text{new}} $$ ### Step-by-Step Solution 1. **Given:** Old slab dimensions: $L_1 = 1 \text{ m}$, $B_1 = 20 \text{ cm}$, $H_1 = 1 \text{ cm}$. New slab dimensions: $H_2 = 1 \text{ mm}$, $B_2 = 1 \text{ m}$. 2. **Unify Units:** Convert everything to centimeters (cm) to avoid decimal errors. $L_1 = 1 \text{ m} = 100 \text{ cm}$ $B_1 = 20 \text{ cm}$ $H_1 = 1 \text{ cm}$ $H_2 = 1 \text{ mm} = 0.1 \text{ cm}$ $B_2 = 1 \text{ m} = 100 \text{ cm}$ 3. **Calculate Original Volume:** $$ V_1 = 100 \times 20 \times 1 = 2000 \text{ cm}^3 $$ 4. **Set Up Equation for New Slab:** $$ V_2 = L_2 \times B_2 \times H_2 $$ $$ 2000 = L_2 \times 100 \times 0.1 $$ $$ 2000 = 10 \times L_2 $$ $$ L_2 = \frac{2000}{10} = 200 \text{ cm} $$ ### Exam Strategy & Shortcut Observe the dimensions: $L_1$ and $B_2$ are both 1m, so they cancel each other out in the volume equation. You just need to solve $20 \text{ cm} \times 1 \text{ cm} = L_2 \times 0.1 \text{ cm}$, making $L_2 = 20 / 0.1 = 200$. ### Common Pitfall Failing to convert millimeters (mm) to centimeters (cm) correctly. Mixing $m, cm$, and $mm$ in a single equation guarantees an incorrect order of magnitude. ### Final Answer Therefore, the correct answer is **200 cm**.