下图显示了一个空容器。所有棱均以直角相交。打开水龙头后,水以每分钟 2.01 升的速度流入容器。完全注满该容器需要多少时间? 答:___

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完整解法

7

1. Decompose the container into two cuboids and find their dimensions.

Let the container be split vertically into a taller cuboid and a shorter cuboid.
Length of the shorter cuboid = 2424 cm.
Length of the taller cuboid = 42−24=1842 - 24 = 18 cm.
Height of the taller cuboid = 8585 cm.
Height of the shorter cuboid = 2020 cm.
Width of both cuboids = 1414 cm.

2. Calculate the total volume of the container in cubic centimetres.

Volume of taller cuboid = 18×14×85=21420 cm318 \times 14 \times 85 = 21420 \text{ cm}^3
Volume of shorter cuboid = 24×14×20=6720 cm324 \times 14 \times 20 = 6720 \text{ cm}^3
Total volume = 21420+6720=28140 cm321420 + 6720 = 28140 \text{ cm}^3

3. Convert the volume to litres and calculate the time needed.

Total volume in litres = 28140÷1000=28.1428140 \div 1000 = 28.14 litres.
Time needed = 28.142.01=14\frac{28.14}{2.01} = 14 minutes.

答案

1111 minutes

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