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在1996年南明区小学毕业考试数试卷上有这样一道题:“一堆小麦堆成圆锥体。量得底面半径是2米,高是1.5米,这堆小麦的体积有多大?大部分学生都能正确地计算。但也有一些学生他们这样计算: 3.14×2~2×1.5=12.56×1.5=18.84(立方米) 显然错了。不难看出,求圆锥的体积,没有乘以1/3。阅卷老师们无不为之感到惋惜和遗憾。 近几年来,我们很多老师非常重视圆锥体积的教学,实践中总结出一些行之有效的能加深学生记忆的求圆锥体积的教学方法。 如一位老师是这样教学的:老师用空心圆柱体满水,说明:水的体积就是圆柱体的体积。再拿一个实心圆锥(和圆柱体等底等高),然后把它插入装有水的圆柱中,排出了一定数量的水,说明排出的水就是圆锥体的体积。取出圆锥,进一步观察讨论,圆柱体高的刻度,从原有水位12厘米,降至现在水位8厘米,降低了1/3。为证实这一结论是否正确,教师再作进一步验
In 1996, Nanming District Elementary School graduation exam papers have such a question: "a pile of wheat piled into a cone. Measuring the bottom radius is 2 meters high is 1.5 meters, the size of the pile of wheat how much? Most students However, there are some students who calculate this way: 3.14 × 2 ~ 2 × 1.5 = 12.56 × 1.5 = 18.84 (m3) Obviously wrong, it is easy to see that the volume of the cone is not multiplied by 1/3. In the recent years, many of our teachers attach great importance to the teaching of conical volume, and in practice, summed up some effective methods of teaching students who can deepen the memory of students seeking conical volume.If a teacher is a This teaching: the teacher with a hollow cylinder filled with water, that the volume of water is the volume of the cylinder, then take a solid cone (cylinder and so the end of the contour), and then put it into the cylinder filled with water, discharge A certain amount of water, indicating that the volume of water discharged is the cone. Remove the cone, further observation and discussion, the cylinder of the high scale, from the original water level of 12 cm, down to 8 cm now, a decrease of 1 / 3. To confirm Is this conclusion positive? Indeed, teachers make further tests