The number of marble slabs of size 20 cm $\times$ 30 cm required to pave the floor of a square room of side 3 metres is

### Concept & Unit Conversion When dealing with geometric quantities like area, ensure all measurements are in the same units before dividing the total area by the unit area. $$ 1 \text{ m} = 100 \text{ cm} \Rightarrow 1 \text{ sq. m} = 10000 \text{ sq. cm} $$ ### Step-by-Step Solution 1. **Convert the room dimensions to cm:** - Side of square room = $3$ m = $300$ cm. 2. **Calculate the area of the floor:** - $\text{Total Area} = 300 \times 300 = 90000$ sq. cm. 3. **Calculate the area of one marble slab:** - $\text{Slab Area} = 20 \text{ cm} \times 30 \text{ cm} = 600$ sq. cm. 4. **Calculate the number of slabs:** - $\text{Number of Slabs} = \frac{\text{Total Area}}{\text{Slab Area}} = \frac{90000}{600} = 150$. ### Exam Strategy & Shortcut You don't need to calculate large areas explicitly. Set up the fraction and cancel out terms: $\frac{300 \times 300}{20 \times 30}$. The zeros cancel: $\frac{30 \times 30}{2 \times 3} = \frac{900}{6} = 150$. ### Common Pitfall A frequent mistake is not squaring the conversion factor when converting square meters to square centimeters (e.g., using $900$ sq. cm instead of $90000$ sq. cm). ### Final Answer Therefore, the correct answer is **150**.