The number of circular pipes with an inside diameter of 1 inch which will carry the same amount of water as a pipe with an inside diameter of 6 inches is

### Concept & Cross-Sectional Area The amount of water a pipe can carry at a given flow velocity is directly proportional to its cross-sectional area, which is proportional to the square of its diameter. $$ \text{Capacity} \propto d^2 $$ ### Step-by-Step Solution * Let the number of 1-inch pipes be $n$. * Area of the 6-inch pipe = $\pi \times (\frac{6}{2})^2 \propto 6^2 = 36$. * Area of a 1-inch pipe = $\pi \times (\frac{1}{2})^2 \propto 1^2 = 1$. * To carry the same amount of water, $n \times 1 = 36 \Rightarrow n = 36$. ### Exam Strategy & Shortcut Since flow capacity is proportional to the area (and thus to diameter squared), simply square the ratio of the diameters: $(\frac{6}{1})^2 = 36$. ### Common Pitfall Assuming the capacity is directly proportional to the diameter rather than the square of the diameter, leading to an incorrect answer of 6. ### Final Answer Therefore, the correct answer is **36**.