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题例一:一个长方体水槽,长10 dm,宽8 dm,水深3 dm。将一个棱长4 dm的正方体铁块放进水槽后,这时水槽内的水深是多少分米?一般来说,学生看到这道题后,会面露喜色,纷纷低头解题。一会儿工夫就会上交作业:(4×4×4)÷(10×8)+3=3.8(dm)。可是,这个结论是错误的。对此,大部分学生会不知所以然。本题一眼望之,与学生平时所做的题没啥两样。其实深入思考后,却另有玄机。学生上述解答的条件是铁块应完全被水淹没,而4 dm高的铁块是否能够在此水槽中全部淹没呢?我们不得而知,问题也由此产生。
Example 1: A cuboid tank, 10 dm long, 8 d wide and 3 dm deep. After putting a cube iron with a length of 4 dm into the sink, how many decimeters is the depth of water in the sink? Generally, students will meet with each other after seeing the title. A little while will be handed over to homework: (4 × 4 × 4) ÷ (10 × 8) +3 = 3.8 (dm). However, this conclusion is wrong. Most students will not know why. This question at a glance, with the students usually did nothing different. In fact, in-depth thinking, but otherwise mysterious. The answer to the above condition is that the iron block should be completely submerged in water. Can the iron block with a height of 4 dm be completely submerged in this water tank? We do not know that the problem arises.