Given that 1 cu. cm of marble weighs 25 gms, the weight of a marble block 28 cm in width and 5 cm thick is 112 kg. The length of the block is

### Concept & Volume-Weight Relationship The weight of a solid block is directly proportional to its volume, based on its material density. $$\text{Total Volume} = \frac{\text{Total Weight}}{\text{Weight per unit Volume}}$$ ### Step-by-Step Solution * **Given:** Width ($b$) = $28 \text{ cm}$, Thickness/Height ($h$) = $5 \text{ cm}$. Total weight = $112 \text{ kg} = 112,000 \text{ gms}$. Weight of $1 \text{ cm}^3 = 25 \text{ gms}$. * **Step 1: Find the total volume of the marble block** $\text{Volume} = \frac{112,000 \text{ gms}}{25 \text{ gms/cm}^3} = 4480 \text{ cm}^3$. * **Step 2: Solve for the unknown length** $\text{Volume} = l \times b \times h$ $4480 = l \times 28 \times 5$ $4480 = l \times 140$ $l = \frac{4480}{140} = 32 \text{ cm}$. ### Exam Strategy & Shortcut To quickly divide $112000$ by $25$, multiply both by $4$: $112000 \times 4 = 448000$, then drop two zeros to get $4480$. From there, $4480 / (28 \times 5)$ simplifies to $4480 / 140 = 448 / 14 = 32$. ### Common Pitfall Failing to convert the total weight from kilograms to grams before dividing by the density in grams. Dividing $112 / 25$ directly will result in a completely incorrect decimal value. ### Final Answer Therefore, the correct answer is **32 cm**.