How many cubes of 3 cm edge can be cut out of a cube of 18 cm edge?

### Concept & Volume Ratio When smaller objects are cut from a larger solid, the number of objects is found by dividing the total volume by the volume of one smaller object. $$ \text{Number of Cubes} = \frac{\text{Volume of Large Cube}}{\text{Volume of Small Cube}} $$ ### Step-by-Step Solution * Volume of the larger cube with $18\text{ cm}$ edge = $18^3\text{ cm}^3$. * Volume of the smaller cube with $3\text{ cm}$ edge = $3^3\text{ cm}^3$. * Divide the volumes: $\frac{18^3}{3^3} = \left(\frac{18}{3}\right)^3$. * Simplify the ratio: $6^3 = 216$. ### Exam Strategy & Shortcut Instead of calculating $18^3$, simply divide the linear edges first: $\frac{18}{3} = 6$. Then cube this linear ratio: $6^3 = 216$. This avoids large numbers entirely. ### Common Pitfall Squaring the ratio instead of cubing it (e.g., doing $6^2 = 36$) because of confusion with surface area formulas. ### Final Answer Therefore, the correct answer is **216**.