正方体铁块熔铸成圆锥形问题

  • 时间:2020-05-23 15:41:47
  • 分类:数学世界
  • 阅读:101 次

正方体铁块熔铸成圆锥形问题:把一块棱长10厘米的正方体铁块熔铸成一个底面直径是20厘米的圆锥形铁块。这个圆锥形铁块的高约是多少厘米?

数学题解答:铁块熔铸前后的形状改变了,但体积并没有改变,所以正方体的体积与圆锥形的体积相等,算出了正方体的体积,就知道了圆锥体的体积,最后根据“圆锥的体积=1/3 × 底面积 × 高”可以推出“圆锥的高=圆锥体积 ÷ 1/3 ÷ 底面积”。

算式如下:

正方体的体积(也是圆锥的体积):10×10×10=1000(立方厘米)

圆锥的底面积:3.14×(20÷2)2=314(平方厘米)

圆锥的高:1000 ÷ 1/3 ÷ 314 ≈9.55(厘米)

答:这个圆锥的高大约是9.55厘米。

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