数学题:水面高度正好是圆锥高度的一半

  • 时间:2020-05-05 19:39:23
  • 分类:数学世界
  • 阅读:91 次

数学题:圆锥形的容积是16升,容器中已有一些水,水面高度正好是圆锥高度的一半,容器中有水多少升?

圆锥装水一半

数学题解答:当水深是圆锥高度的一半时,水面的半径也是圆锥底面半径的一半。如果圆锥的底面半径为r,高为h,则装水部分的底面半径是1/2 r,高是1/2 h。

体积V=1/3 ∏ (1/2* r)2 1/2*h=1/3 ∏ r2h × 1/8

如果看不懂这里,也可以理解为:圆锥的体积=1/3×圆周率×半径2×高,所以水的体积是圆锥容器体积的:1/2 * 1/2 * 1/2 = 1/8。

即水的体积是圆锥容器容积的1/8。

所以水的体积是:16 × 1/8 = 2(升)

答:容器中有水2升。

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