Calculating River Water Quantity Per Minute

The question asks for the volume of water flowing into the sea per minute. We can calculate this by finding the volume of a rectangular prism of water that passes a point in one minute. The dimensions of this prism are the river's width, depth, and the distance the water travels in one minute.

1. Identify Given Information

• River Depth: $d = 2$ m
• River Width: $w = 45$ m
• Flow Speed: $v = 3$ km per hour

2. Convert Flow Speed to Meters Per Minute

To calculate the volume in cubic meters per minute, we need the speed in meters per minute.

• $1$ km $= 1000$ m
• $1$ hour $= 60$ minutes
• Speed $v = 3 \frac{\text{km}}{\text{hour}} = 3 \times \frac{1000 \text{ m}}{60 \text{ min}} = \frac{3000}{60} \frac{\text{m}}{\text{min}} = 50$ m/min.

3. Calculate the Cross-Sectional Area of the River

The cross-sectional area ($A$) is the product of the river's depth and width.

• $A = \text{depth} \times \text{width} = d \times w
• $A = 2 \text{ m} \times 45 \text{ m} = 90 \text{ m}^2$.

4. Calculate Volume of Water Per Minute

The volume of water flowing per minute ($V_{min}$) is the cross-sectional area multiplied by the distance the water travels in one minute (which is the speed in m/min).

• $V_{min} = A \times v$ (where $v$ is in m/min)
• $V_{min} = 90 \text{ m}^2 \times 50 \text{ m/min}
• $V_{min} = 4500 \text{ m}^3/\text{min}$.

Therefore, the quantity of water that runs into the sea per minute is $4500$ m$^3$. This matches Option A.