A rectangular box measures internally 1.6 m long, 1 m broad and 60 cm deep. The number of cubical blocks each of edge 20 cm that can be packed inside the box is

### Concept & 3D Packing To find out how many blocks can fit inside a box, ensure the dimensions of the blocks divide evenly into the dimensions of the box. If they do, simply divide the total volume by the volume of one block. $$ \text{Number of Blocks} = \frac{\text{Internal Volume of Box}}{\text{Volume of One Block}} $$ ### Step-by-Step Solution * Convert all dimensions of the rectangular box to the same unit (centimeters): * Length = $1.6\text{ m} = 160\text{ cm}$ * Breadth = $1\text{ m} = 100\text{ cm}$ * Depth = $60\text{ cm}$ * Check divisibility to ensure perfect packing: * Length: $\frac{160}{20} = 8$ blocks * Breadth: $\frac{100}{20} = 5$ blocks * Depth: $\frac{60}{20} = 3$ blocks * Since all dimensions perfectly accommodate the $20\text{ cm}$ edges, no space is wasted. * Multiply the number of blocks along each dimension to find the total: $8 \times 5 \times 3 = 120$ blocks. ### Exam Strategy & Shortcut Avoid calculating massive volumes. Instead, divide each dimension of the large box by the side length of the cube: $\frac{160}{20} \times \frac{100}{20} \times \frac{60}{20} = 8 \times 5 \times 3 = 120$. This keeps the numbers small and manageable. ### Common Pitfall Calculating the volumes first ($160 \times 100 \times 60 = 960,000$ and $20^3 = 8,000$) creates large numbers which increase the likelihood of a division error (e.g., mistaking the number of zeros). ### Final Answer Therefore, the correct answer is **120**.