一个长方体水槽起初装有一些水。然后打开水龙头，将水槽完全注满水。水龙头在 48 分钟结束时被关闭。下图显示了 48 分钟内水槽中的水量。

  1. (a)

    每分钟有多少升水从水龙头流出？

  2. (b)

    到 48 分钟结束时，水槽溢出了多少升水？

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完整解法

7(a)

1. Identify the initial and final volume of water during the filling phase from the graph

From the graph, at t=0t = 0 min, the volume is 2020 L.
The tank is completely filled at t=24t = 24 min, where the volume is 110110 L.

2. Calculate the total volume of water that flowed from the tap

Total volume flowed = 110−20=90110 - 20 = 90 L

3. Calculate the rate of water flow per minute

Rate = 9024=3.75\frac{90}{24} = 3.75 L/min

答案

3.753.75 litres

7(b)

1. Determine the duration for which the water overflowed

The tank is completely filled at 2424 minutes. The tap was turned off at 4848 minutes.
Time during which water overflowed = 48−24=2448 - 24 = 24 minutes.

2. Calculate the volume of water that overflowed

From the graph, the amount of water that flowed from the tap in the first 2424 minutes is 110−20=90110 - 20 = 90 L.
Since the tap flows at a constant rate, the amount of water that flowed (and overflowed) in the next 2424 minutes is also 9090 L.
Alternatively, using the rate from part (a) (3.753.75 L/min):
Volume overflowed = 3.75×24=903.75 \times 24 = 90 L.

答案

9090 L

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