How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?

### Concept & Volume Division To find how many smaller 3D objects fit into a larger one perfectly, divide the volume of the larger object by the volume of the smaller object, provided their dimensions align evenly. $$ \text{Number of Objects} = \frac{\text{Total Volume}}{\text{Volume of One Object}} $$ ### Step-by-Step Solution * Convert dimensions to the same unit: The larger cubical box has an edge of $1\text{ m}$. Convert this to centimeters: $1\text{ m} = 100\text{ cm}$. * Calculate the volume of the larger box: $100\text{ cm} \times 100\text{ cm} \times 100\text{ cm} = 1,000,000\text{ cm}^3$. * Calculate the volume of one smaller cube: $10\text{ cm} \times 10\text{ cm} \times 10\text{ cm} = 1,000\text{ cm}^3$. * Divide the volumes: $\frac{1,000,000}{1,000} = 1000$ cubes. * Alternatively, divide the edges: $\frac{100\text{ cm}}{10\text{ cm}} = 10$ cubes per side. Total cubes = $10 \times 10 \times 10 = 1000$. ### Exam Strategy & Shortcut Find how many small cubes fit along one edge: $\frac{1\text{ m}}{10\text{ cm}} = \frac{100}{10} = 10$. Since it's a cube, cube this number: $10^3 = 1000$. ### Common Pitfall Failing to convert meters to centimeters correctly before cubing, or squaring instead of cubing the linear ratio. ### Final Answer Therefore, the correct answer is **1000**.