Shobhraj takes a cube of 1 m edge-length and meticulously cuts smaller cubes, each of edge-length 1 mm from the parent cube. He joins these small cubes end-to-end. Thus, the total length of this 'cube-robe' will be

### Concept & Conservation of Volume The total volume of the cut smaller cubes is exactly equal to the volume of the original large cube. The total length of the joined cubes depends on how many small cubes are formed. $$ \text{Total Length} = \text{Number of Cubes} \times \text{Edge Length of Small Cube} $$ ### Step-by-Step Solution * Convert the parent cube's edge to millimeters: $1\text{ m} = 1000\text{ mm}$. * Calculate the total volume in $\text{mm}^3$: Volume = $(1000\text{ mm})^3 = 1,000,000,000\text{ mm}^3$ (or $10^9\text{ mm}^3$). * Since each small cube has a volume of $1\text{ mm}^3$, the number of small cubes is $10^9$. * Joining them end-to-end means multiplying the number of cubes by the edge length of one cube ($1\text{ mm}$): Total length = $10^9 \times 1\text{ mm} = 10^9\text{ mm}$. * Convert millimeters back to meters: $10^9\text{ mm} = 10^6\text{ meters}$. * Convert meters to kilometers: $10^6\text{ m} = 1000\text{ km}$. ### Exam Strategy & Shortcut Number of cubes = $(1000)^3 = 10^9$. Length in mm = $10^9\text{ mm}$. To convert mm to km directly, shift the decimal 6 places (3 for meters, 3 for km). $10^9 / 10^6 = 10^3 = 1000\text{ km}$. ### Common Pitfall Mistaking the conversion factors, such as assuming $1\text{ m} = 100\text{ mm}$ instead of $1000\text{ mm}$, leading to an answer of 1 km or 10 km. ### Final Answer Therefore, the correct answer is **1000 km**.