It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 440 cubic metres in 10 minutes. The inner radius of the pipe should be

### Concept & Volume of a Cylinder The volume of water flowing through a pipe in a given time equals the cross-sectional area of the pipe multiplied by the length of the water column (speed $\times$ time). $$ \text{Volume} = \pi \times r^2 \times (\text{Speed} \times \text{Time}) $$ ### Step-by-Step Solution * Given: Speed = 7 m/min, Time = 10 min, Volume = $440 \text{ m}^3$. * The length of the water column ($h$) formed in 10 minutes is $7 \times 10 = 70 \text{ m}$. * Using the volume formula: $\frac{22}{7} \times r^2 \times 70 = 440$. * $220 \times r^2 = 440 \Rightarrow r^2 = 2$. * $r = \sqrt{2} \text{ m}$. ### Exam Strategy & Shortcut When dealing with speed of flow, treat speed as the height of the cylinder per unit time. Multiply by total time to get total equivalent height. ### Common Pitfall Forgetting to calculate the total length of the water column over the 10 minutes and just using the speed per minute. ### Final Answer Therefore, the correct answer is **$\sqrt{2}$ m**.