If a river $2.5 \text{ m}$ deep and $45 \text{ m}$ wide is flowing at the rate of $3.6 \text{ km}$ per hour, then the amount of water that runs into the sea per minute is

### Concept & Formula The volume of water flowing through a cross-section in a given time equals the area of the cross-section multiplied by the distance the water travels in that time (speed). $$ \text{Volume per minute} = \text{Width} \times \text{Depth} \times \text{Speed per minute} $$ ### Step-by-Step Solution 1. **Convert the speed to meters per minute:** $\text{Speed} = 3.6 \text{ km/hr} = 3600 \text{ m} / 60 \text{ min} = 60 \text{ m/min}$ 2. **Calculate the cross-sectional area of the river:** $\text{Area} = 2.5 \text{ m (depth)} \times 45 \text{ m (width)} = 112.5 \text{ m}^2$ 3. **Calculate the volume per minute:** $\text{Volume} = \text{Area} \times \text{Speed per minute}$ $\text{Volume} = 112.5 \text{ m}^2 \times 60 \text{ m/min} = 6750 \text{ m}^3$ ### Exam Strategy & Shortcut Recognize that $3.6 \text{ km/hr} = 1 \text{ m/s}$. Since we need the volume per minute, the speed is simply $1 \text{ m/s} \times 60 \text{ s} = 60 \text{ m/min}$. Multiply $45 \times 2.5 \times 60 \implies 45 \times 150 = 6750$. ### Common Pitfall Failing to convert the time and distance units uniformly before multiplying (e.g., mixing km/hr with meters). ### Final Answer Therefore, the correct answer is **6750 cu. m**.