The diameter of the base of a cylindrical drum is 35 dm and the height is 24 dm. It is full of kerosene. How many tins each of size 25 cm $\times$ 22 cm $\times$ 35 cm can be filled with kerosene from the drum?

### Concept & Object Count To find how many small containers fit into a large one, divide the total volume by the volume of one small container. Number of tins = $\frac{\text{Volume of Drum}}{\text{Volume of one Tin}}$ **Crucial:** Ensure all units match before calculating. $1 \text{ dm} = 10 \text{ cm}$. ### Step-by-Step Solution * **Given Drum:** Diameter = 35 dm = 350 cm, so Radius ($r$) = 175 cm. Height ($H$) = 24 dm = 240 cm. * **Given Tin:** Dimensions = 25 cm $\times$ 22 cm $\times$ 35 cm. * Setup the equation for the number of tins ($N$): $$N = \frac{\pi r^2 H}{L \times B \times h}$$ $$N = \frac{\frac{22}{7} \times 175 \times 175 \times 240}{25 \times 22 \times 35}$$ * Simplify by cancelling terms. The 22 in numerator and denominator cancel out: $$N = \frac{\frac{1}{7} \times 175 \times 175 \times 240}{25 \times 35}$$ * Simplify $\frac{175}{7} = 25$: $$N = \frac{25 \times 175 \times 240}{25 \times 35}$$ * Cancel the 25s: $$N = \frac{175 \times 240}{35}$$ * Simplify $\frac{175}{35} = 5$: $$N = 5 \times 240 = 1200$$ ### Exam Strategy & Shortcut Do not multiply everything out to find the total volumes. Write the full fraction and cross out numbers diagonally. This minimizes calculation effort and eliminates large arithmetic errors. ### Common Pitfall Failing to convert dm to cm. If left in dm, the calculation becomes severely mismatched, producing an answer off by a factor of 1000. ### Final Answer Therefore, the correct answer is **1200**.